almost equitable partitions and new necessary conditions for network controllability abstract in this paper we consider the controllability problem for multi agent networked control systems the main results of the paper are new graph theoretic necessary conditions for controllability involving almost equitable graph vertex partitions we generalize the known results on the role of graph symmetries and uncontrollability to weighted digraphs with multiple leaders and we also consider the broadcasted control scenario our results show that the internal structure of communities in a graph can induce obstructions to controllability that cannot be characterized by symmetry arguments alone and that in some cases depend on the number theoretic properties of the communities we show via examples that our results can be used to account for a large portion of uncontrollable inducing leader selections that could not have otherwise been accounted for using symmetry results

optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes in multivariate matching fine balance constrains the marginal distributions of a nominal variable in treated and matched control groups to be identical without constraining who is matched to whom in this way a fine balance constraint can balance a nominal variable with many levels while focusing efforts on other more important variables when pairing individuals to minimize the total covariate distance within pairs fine balance is not always possible that is it is a constraint on an optimization problem but the constraint is not always feasible we propose a new algorithm which returns a minimum distance finely balanced match when one is feasible and otherwise minimizes the total distance among all matched samples that minimize the deviation from fine balance perhaps we can come very close to fine balance when fine balance is not attainable moreover in any event because our algorithm is guaranteed to come as close as possible to fine balance the investigator may perform one match and on that basis judge whether the best attainable balance is adequate or not we also show how to incorporate an additional constraint the algorithm is implemented in two similar ways first as an optimal assignment problem with an augmented distance matrix second as a minimum cost flow problem in a network the case of knee surgery in the obesity and surgical outcomes study motivated the development of this algorithm and is used as an illustration in that example two of 47 hospitals had too few nonobese patients to permit fine balance for the nominal variable with 47 levels representing the hospital but our new algorithm came very close to fine balance moreover in that example there was a shortage of nonobese diabetic patients and incorporation of an additional constraint forced the match to include all of these nonobese diabetic patients thereby coming as close as possible to balance for this important but recalcitrant covariate

general and refined montgomery lemmata montgomery s lemma on the torus mathbb t d states that a sum of n dirac masses cannot be orthogonal to many low frequency trigonometric functions in a quantified way we provide an extension to general manifolds that also allows for positive weights let m g be a smooth compact d dimensional manifold without boundary let phi k k 0 infty denote the laplacian eigenfunctions let left x 1 dots x n right subset m be a set of points and left a 1 dots a n right subset mathbb r ge 0 be a sequence of nonnegative weights then for all x ge 0 begin aligned sum k 0 x left sum n 1 n a n phi k x n right 2 gtrsim m g left sum i 1 n a i 2 right frac x log x frac d 2 end aligned this result is sharp up to the logarithmic factor furthermore we prove a refined spherical version of montgomery s lemma and provide applications to estimates of discrepancy and discrete energies of n points on the sphere mathbb s d

exact nonparametric inference when doses are measured with random errors studies that estimate the effects of exposure to a possibly harmful agent often compare exposed subjects who received varied doses with matched controls who received zero dose if the doses are measured with error then one may wish to use the fallible doses to estimate a linear relationship between the unobserved true dose and the observed response if one is willing to assume that the dose errors for exposed subjects are symmetrically distributed about 0 that is the dose errors are pure errors and not say systematic underreporting of exposure then the presence of zero dose controls is all that is needed to obtain exact distribution free confidence intervals and tests and consistent point estimates the method is simpler for matched pairs than for matched sets with two or more matched subjects and it is illustrated using two studies one of each kind with matched pairs as in this first example the method uses wilcoxon s signed rank test as the basis for inference when there are several zero dos

higher order properties of gmm and generalized empirical likelihood estimators in an effort to improve the small sample properties of generalized method of moments gmm estimators a number of alternative estimators have been suggested these include empirical likelihood el continuous updating and exponential tilting estimators we show that these estimators share a common structure being members of a class of generalized empirical likelihood gel estimators we use this structure to compare their higher order asymptotic properties we find that gel has no asymptotic bias due to correlation of the moment functions with their jacobian eliminating an important source of bias for gmm in models with endogeneity we also find that el has no asymptotic bias from estimating the optimal weight matrix eliminating a further important source of bias for gmm in panel data models we give bias corrected gmm and gel estimators we also show that bias corrected el inherits the higher order property of maximum likelihood that it is higher order asymptotically efficient relative to the other bias corrected estimators

using empirical likelihood methods to obtain range restricted weights in regression estimators for surveys design weights in surveys are often adjusted to accommodate auxiliary information and to meet pre specified range restrictions typically via some ad hoc algorithmic adjustment to a generalised regression estimator in this paper we present a simple solution to this problem using empirical likelihood methods or generalised regression we first develop algorithms for computing empirical likelihood estimators and model calibrated empirical likelihood estimators the first algorithm solves the computational problem of the empirical likelihood method in general both in survey and non survey settings and theoretically guarantees its convergence the second exploits properties of the model calibration method and is particularly simple the algorithms are adapted for handling benchmark constraints and pre specified range restrictions on the weight adjustments

point estimation with exponentially tilted empirical likelihood parameters defined via general estimating equations gee can be estimated by maximizing the empirical likelihood el newey and smith econometrica 72 2004 219 255 have recently shown that this el estimator exhibits desirable higher order asymptotic properties namely that its o n 1 bias is small and that bias corrected el is higher order efficient although el possesses these properties when the model is correctly specified this paper shows that in the presence of model misspecification el may cease to be root n convergent when the functions defining the moment conditions are unbounded even when their expectations are bounded in contrast the related exponential tilting et estimator avoids this problem this paper shows that the et and el estimators can be naturally combined to yield an estimator called exponentially tilted empirical likelihood etel exhibiting the same o n 1 bias and the same o n 2 variance as el while maintaining root n convergence under model misspecification

on the controllability properties of circulant networks this paper examines the controllability of a group of first order agents adopting a weighted consensus type coordination protocol over a circulant network specifically it is shown that a circulant network with laplacian eigenvalues of maximum algebraic multiplicity q is controllable from q nodes our approach leverages on the cauchy binet formula which in conjunction with the popov belevitch hautus test leads to new insights on structural aspects of network controllability

controllability of multi agent systems with periodically switching topologies and switching leaders abstractthis paper considers controllability of multi agent systems with periodically switching topologies and switching leaders the concept of m periodic controllability is proposed and a criterion for m periodic controllability is established the effect of the duration of subsystems on controllability is analysed by utilising a property of analytic functions in addition the influence of switching periods on controllability is investigated and an algorithm is proposed to search for the fewest periods to ensure controllability a necessary condition for m periodic controllability is obtained from the perspective of eigenvectors of the subsystems laplacian matrices for a system with switching leaders it is proved that switching leader controllability is equivalent to multiple leader controllability furthermore both the switching order and the tenure of agents being leaders have no effect on the controllability some examples are provided to illustrate the theoretical results

globally efficient non parametric inference of average treatment effects by empirical balancing calibration weighting the estimation of average treatment effects based on observational data is extremely important in practice and has been studied by generations of statisticians under different frameworks existing globally efficient estimators require non parametric estimation of a propensity score function an outcome regression function or both but their performance can be poor in practical sample sizes without explicitly estimating either functions we consider a wide class calibration weights constructed to attain an exact three way balance of the moments of observed covariates among the treated the control and the combined group the wide class includes exponential tilting empirical likelihood and generalized regression as important special cases and extends survey calibration estimators to different statistical problems and with important distinctions global semiparametric efficiency for the estimation of average treatment effects is established for this general class of calibration estimators the results show that efficiency can be achieved by solely balancing the covariate distributions without resorting to direct estimation of propensity score or outcome regression function we also propose a consistent estimator for the efficient asymptotic variance which does not involve additional functional estimation of either the propensity score or the outcome regression functions the proposed variance estimator outperforms existing estimators that require a direct approximation of the efficient influence function

controllability of heterogeneous multi agent systems under directed and weighted topology abstractthis paper considers the controllability problem for both continuous and discrete time linear heterogeneous multi agent systems with directed and weighted communication topology first two kinds of neighbour based control protocols based on the distributed protocol of first order and second order multi agent systems are proposed under which it is shown that a heterogeneous multi agent system is controllable if the underlying communication topology is controllable then under special leader selection the result shows that the controllability of a heterogeneous multi agent system is solely decided by its communication topology graph furthermore some necessary and or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives finally simulation examples are presented to demonstrate the effectiveness of the theoretical results

empirical likelihood and general estimating equations for some time so called empirical likelihoods have been used heuristically for purposes of nonparametric estimation owen showed that empirical likelihood ratio statistics for various parameters theta f of an unknown distribution f have limiting chi square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods our objective in this paper is twofold first to link estimating functions or equations and empirical likelihood second to develop methods of combining information about parameters we do this by assuming that information about f and theta is available in the form of unbiased estimating functions empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood efficiency results for estimates of both theta and f are obtained the methods are illustrated on several problems and areas for future investigation are noted

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

covariate association eliminating weights a unified weighting framework for causal effect estimation weighting methods offer an approach to estimating causal treatment effects in observational studies however if weights are estimated by maximum likelihood misspecification of the treatment assignment model can lead to weighted estimators with substantial bias and variance in this paper we propose a unified framework for constructing weights such that a set of measured pretreatment covariates is unassociated with treatment assignment after weighting we derive conditions for weight estimation by eliminating the associations between these covariates and treatment assignment characterized in a chosen treatment assignment model after weighting the moment conditions in covariate balancing weight methods for binary categorical and continuous treatments in cross sectional settings are special cases of the conditions in our framework which extends to longitudinal settings simulation shows that our method gives treatment effect estimates with smaller biases and variances than the maximum likelihood approach under treatment assignment model misspecification we illustrate our method with an application to systemic lupus erythematosus data

quadratic stabilisability of multi agent systems under switching topologies this paper addresses the stabilisability of multi agent systems mass under switching topologies necessary and or sufficient conditions are presented in terms of graph topology these conditions explicitly reveal how the intrinsic dynamics of the agents the communication topology and the external control input affect stabilisability jointly with the appropriate selection of some agents to which the external inputs are applied and the suitable design of neighbour interaction rules via a switching topology an mas is proved to be stabilisable even if so is not for each of uncertain subsystem in addition a method is proposed to constructively design a switching rule for mass with norm bounded time varying uncertainties the switching rules designed via this method do not rely on uncertainties and the switched mas is quadratically stabilisable via decentralised external self feedback for all uncertainties with respect to applications of the stabilisability results the formation control and the cooper

relaxation methods for problems with strictly convex separable costs and linear constraints we consider the minimization problem with strictly convex possibly nondifferentiable separable cost and linear constraints the dual of this problem is an unconstrained minimization problem with differentiable cost which is well suited for solution by parallel methods based on gauss seidel relaxation we show that these methods yield the optimal primal solution and under additional assumptions an optimal dual solution to do this it is necessary to extend the classical gauss seidel convergence results because the dual cost may not be strictly convex and may have unbounded level sets

nonparametric estimation of mean functionals with data missing at random abstract this article considers a distribution free estimation procedure for a basic pattern of missing data that often arises from the wellknown double sampling in survey methodology without parametric modeling of the missing mechanism or the joint distribution kernel regression estimators are used to estimate mean functionals through empirical estimation of the missing pattern a generalization of the method of cheng and wei is verified under the assumption of missing at random asymptotic distributions are derived for estimating the mean of the incomplete data and for estimating the mean treatment difference in a nonrandomized observational study the nonparametric method is compared with a naive pairwise deletion method and a linear regression method via the asymptotic relative efficiencies and a simulation study the comparison shows that the proposed nonparametric estimators attain reliable performances in general

a model calibration approach to using complete auxiliary information from survey data suppose that the finite population consists of n identifiable units associated with the ith unit are the study variable yi and a vector of auxiliary variables xi the values x1 x2 xn are known for the entire population i e complete but yi is known only if the ith unit is selected in the sample one of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage in this article a unified model assisted framework has been attempted using a proposed model calibration technique the proposed model calibration estimators can handle any linear or nonlinear working models and reduce to the conventional calibration estimators of deville and sarndal and or the generalized regression estimators in the linear model case the pseudoempirical maximum likelihood estimator of chen and sitter when used in this setting gives an estimator that is asymptotically equivalent to the model calibration estimator but with positive weights some existing estimators

efficient estimation of population level summaries in general semiparametric regression models this article considers a wide class of semiparametric regression models in which interest focuses on population level quantities that combine both the parametric and the nonparametric parts of the model special cases in this approach include generalized partially linear models generalized partially linear single index models structural measurement error models and many others for estimating the parametric part of the model efficiently profile likelihood kernel estimation methods are well established in the literature here our focus is on estimating general population level quantities that combine the parametric and nonparametric parts of the model e g population mean probabilities etc we place this problem in a general context provide a general kernel based methodology and derive the asymptotic distributions of estimates of these population level quantities showing that in many cases the estimates are semiparametric efficient for estimating the population mean with no missing data we s

kernel based covariate functional balancing for observational studies covariate balance is often advocated for objective causal inference since it mimics randomization in observational data unlike methods that balance specific moments of covariates our proposal attains uniform approximate balance for covariate functions in a reproducing kernel hilbert space the corresponding infinite dimensional optimization problem is shown to have a finite dimensional representation in terms of an eigenvalue optimization problem large sample results are studied and numerical examples show that the proposed method achieves better balance with smaller sampling variability than existing methods

performance and design of cycles in consensus networks abstract this work explores the role of cycles in consensus seeking networks for analysis and synthesis purposes cycles are critical for many reasons including improving the convergence rate of the system resilience to link failures and the overall performance of the system the focus of this work examines how cycles impact the h 2 performance of consensus networks a first contribution shows that the addition of cycles always improves the performance of the system we provide an analytic characterization of how the addition of edges improves the performance and show that it is related to the inverse of the cycle lengths and the number of shared edges between independent cycles these results are then used to consider the design of consensus networks in this direction we present an l 1 relaxation method that leads to a convex program for adding a fixed number of edges to a consensus networks we also demonstrate how this relaxation can be used to embed additional performance criteria such as maximization of the algebraic connectivity of the graph

laplacian controllability classes for threshold graphs abstract let g be a graph on n vertices with laplacian matrix l and let b be a binary vector of length n the pair l b is controllable if the smallest l invariant subspace containing b is of dimension n the graph g is called essentially controllable if l b is controllable for every b ker l completely uncontrollable if l b is uncontrollable for every b and conditionally controllable if it is neither essentially controllable nor completely uncontrollable in this paper we completely characterize the graph controllability classes for threshold graphs we first observe that the class of threshold graphs contains no essentially controllable graph we prove that a threshold graph is completely uncontrollable if and only if its laplacian matrix has a repeated eigenvalue in the process we fully characterize the set of conditionally controllable threshold graphs

zero forcing sets and controllability of dynamical systems defined on graphs in this technical note controllability of systems defined on graphs is discussed we consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph a one to one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established to illustrate the proposed results special cases including path cycle and complete graphs are discussed moreover as shown for graphs with a tree structure the proposed results of the present technical note together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases

controllability of the multi agent system modeled by the threshold graph with one repeated degree abstract the controllability issue of multi agent systems modeled by a special class of graphs is studied suppose the modeling graph is simple connected and driven by only one controller the author shows that the system is controllable if the graph has exactly two vertices with the same degree and either one of these two vertices is selected to receive the control input this result is extended to the case of the threshold graph that has only one repeated degree specifically it is shown that if the threshold graph has only one repeated degree and its multiplicity is m then m 1 is the minimum number of the controllers required to make the system controllable in addition the necessary and sufficient condition that characterizes the binary control vectors to ensure the controllability of the system is derived

observability through a matrix weighted graph observability of an array of identical linear time invariant systems with incommensurable output matrices is studied where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems it is shown that the observability of an array is equivalent to the connectivity of its interconnection graph whose edges are assigned matrix weights moreover to better understand the relative behavior of distant units pairwise observability that concerns with the synchronization of a certain pair of individual systems in the array is studied this milder version of observability is shown to be closely related to certain connectivity properties of the interconnection graph as well pairwise observability is also analyzed using the circuit theoretic tool effective conductance the observability of a certain pair of units is proved to be equivalent to the nonsingularity of the matrix valued effective conductance between the associated pair of nodes of a resistive network with matrix valued parameters whose node admittance matrix is the laplacian of the array s interconnection graph

nodes selection strategy in cooperative tracking problem in this paper a new optimization problem is addressed for node selection that has application potentials in input output switches for sensors in control system design and leader determination in social networks the purpose of the addressed problem is to develop a strategy for selecting a subset of nodes as controlled nodes in order to minimize certain objective function consisting of the convergence speed and the energy of control action over a finite time horizon for networks with fixed controlled nodes an upper bound of the objective function is obtained which is shown to be convex and independent of the time horizon for networks with switched controlled nodes a greedy algorithm is proposed to reduce the computation complexity resulting from the length of the time horizon where the nodes selection is carried out over divided small time intervals the cost gap is also analyzed between the strategy of optimizing over the whole time horizon and the strategy of optimizing over the small intervals finally the proposed nodes selection strategy is validated through simulations and two regions are found in which the number of optimal controlled nodes is determined

bounded efficient and doubly robust estimation with inverse weighting consider estimating the mean of an outcome in the presence of missing data or estimating population average treatment effects in causal inference a doubly robust estimator remains consistent if an outcome regression model or a propensity score model is correctly specified we build on a previous nonparametric likelihood approach and propose new doubly robust estimators which have desirable properties in efficiency if the propensity score model is correctly specified and in boundedness even if the inverse probability weights are highly variable we compare the new and existing estimators in a simulation study and find that the robustified likelihood estimators yield overall the smallest mean squared errors

upper and lower bounds for controllable subspaces of networks of diffusively coupled agents this technical note studies the controllability of diffusively coupled networks where some agents called leaders are under the influence of external control inputs first we consider networks where agents have general linear dynamics then we turn our attention to infer network controllability from its underlying graph topology to do this we consider networks with agents having single integrator dynamics for such networks we provide lower and upper bounds for the controllable subspaces in terms of the distance partitions and the maximal almost equitable partitions respectively we also provide an algorithm for computing the maximal almost equitable partition for a given graph and a set of leaders

multiply robust estimation in regression analysis with missing data doubly robust estimators are widely used in missing data analysis they provide double protection on estimation consistency against model misspecifications however they allow only a single model for the missingness mechanism and a single model for the data distribution and the assumption that one of these two models is correctly specified is restrictive in practice for regression analysis with possibly missing outcome we propose an estimation method that allows multiple models for both the missingness mechanism and the data distribution the resulting estimator is consistent if any one of those multiple models is correctly specified and thus provides multiple protection on consistency this estimator is also robust against extreme values of the fitted missingness probability which for most doubly robust estimators can lead to erroneously large inverse probability weights that may jeopardize the numerical performance the numerical implementation of the proposed method through a modified newton ra

combining propensity score matching with additional adjustments for prognostic covariates abstract propensity score matching refers to a class of multivariate methods used in comparative studies to construct treated and matched control samples that have similar distributions on many covariates this matching is the observational study analog of randomization in ideal experiments but is far less complete as it can only balance the distribution of observed covariates whereas randomization balances the distribution of all covariates both observed and unobserved an important feature of propensity score matching is that it can be easily combined with model based regression adjustments or with matching on a subset of special prognostic covariates or combinations of prognostic covariates that have been identified as being especially predictive of the outcome variables we extend earlier results by developing approximations for the distributions of covariates in matched samples created with linear propensity score methods for the practically important situation where matching uses both the estimat

on a sharp lemma of cassels and montgomery on manifolds let m g be a d dimensional compact connected riemannian manifold and let m m 0 oo be a complete sequence of orthonormal eigenfunctions of the laplace beltrami operator on m we show that there exists a positive constant c such that for all integers n and x and for all finite sequences of n points in m x j and positive weights a j j 1 n we have a j m x j 2 max c x a j 2 a j 2 in the left hand side the inner sum is for j 1 n and the outer sum is for m 0 x

constructing a controllable graph under edge constraints abstract this paper is concerned with the problem of constructing a controllable graph subject to some practical edge constraints specifically suppose the total amount of vertices and the upper bounds on the graph diameter or on the vertex degree are given we consider the problem of exploring a class of feasible graphs that satisfy the constraints using the hybrid of a path graph and an antiregular graph we propose a simple and systematic method to generate a class of controllable graphs whose diameters or degrees cover the full possible ranges the method to select the control vector to ensure the controllability of the combined graph is also proposed numerical examples are provided to demonstrate our results

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data which involve models for both the propensity score and the regression of outcome on covariates the usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations we propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods even with some estimated propensity scores close to zero

controllability of multiagent networks with antagonistic interactions this paper addresses the controllability of a class of antagonistic multiagent networks with both positive and negative edges all the agents of the multiagent network run a consensus algorithm using a signed laplacian based on the generalized equitable partition we propose a graph theoretic characterization of an upper bound on the controllable subspace then we provide a necessary condition for the controllability of the system and give an algorithm to compute the partition furthermore we prove that for a structurally balanced network the controllability is equivalent to that of the corresponding all positive network if the leaders are chosen from the same vertex set several examples are given to illustrate these results

the usefulness of optimum experimental designs optimum experimental designs were originally developed by kiefer mainly for response surface models this survey of recent developments emphasizes potential or actual usefulness for linear models the construction of exact designs particularly over irregular design regions is stressed as is the blocking of response surface designs other important areas include systematic designs that are robust against trend and designs for mixtures with irregular design regions several industrial examples are mentioned both d and c optimum designs are found for a non linear model of the economic response of cereal production to fertilizer level the c optimum design being for the conditions of maximum economic return locally optimum and bayesian designs are both described similar results for generalized linear models lead to designs for the ld 95 in a logistic model in which male and female subjects respond differently designs with structure in the variance suggest alternatives to the potentially wasteful product designs of taguchi designs for sequential clinical trials to include random balance are presented the last section outlines some applications including life testing and models in which time is a factor

weighted likelihood estimation under two phase sampling we develop asymptotic theory for weighted likelihood esti mators wle under two phase stratied sampling without replacement we also consider several variants of wle s involving estimated weights and calibration a set of empirical process tools are developed including a glivenko cantelli theorem a theorem for rates of convergence of z estimators and a donsker theorem for the inverse probability weighted em pirical processes under two phase sampling and sampling without replace ment at the second phase using these general results we derive asymptotic distributions of the wle of a nite dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is es timable either at regular or non regular rates we illustrate these results and methods in the cox model with right censoring and interval censor ing we compare the methods via their asymptotic variances under both sampling without replacement and the more usual and easier to analyze assumption of bernoulli sampling at the second phase ams 2000 subject classications primary 62e20 secondary 62g20 62d99 62n01

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

large sample properties of matching estimators for average treatment effects matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases the absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data in this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results we focus on matching with replacement with a fixed number of matches first we show that matching estimators are not n 1 2 consistent in general and describe conditions under which matching estimators do attain n 1 2 consistency second we show that even in settings where matching estimators are n 1 2 consistent simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound third we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions software for implementing these methods is available in matlab stata and r

controllability of discrete time multi agent systems with directed topology and input delay this paper investigates the controllability of first order and second order discrete time multi agent systems with directed topology and input delay the problem is studied in the leader follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents sufficient and necessary conditions are derived for the controllability of first order discrete time multi agent systems with sampling period and feedback gain satisfying certain conditions it is proved under three different protocols that the controllability of second order discrete time multi agent systems is equivalent to that of a pair of submatrices of laplacian matrix in addition the controllability of both first order and second order discrete time multi agent systems with input delay is shown through some transformations to be equivalent to that of the transformed non delayed systems finally some simulation examples are given to illustrate the theoretical results

controllability and observability of network of networks via cartesian products the paper presents a system theoretic analysis framework for a network of networks formed from smaller factor networks via graph cartesian products we provide a compositional framework for extending the controllability and observability of the factor networks to that of the composite network of networks we then delve into the effectiveness of designing control and estimation algorithms for the composite network via its symmetry and gramian structure an example demonstrating the usefulness of our results in the context of social networks with a cartesian product structure is then presented

an information theoretic alternative to generalized method of moments estimation while optimally weighted gmm estimation has desirable large sample properties its small sample performance is poor in some applications we propose a computationally simple alternative for weakly dependent data generating mechanisms based on minimization of the kullback leibler information criterion conditions are derived under which the large sample properties of this estimator are similar to gmm i e the estimator will be consistent and asymptotically normal with the same asymptotic covariance matrix as gmm in addition we propose overidentifying and parametric restrictions tests as alternatives to analogous gmm procedures

controllability and observability of grid graphs via reduction and symmetries in this paper we investigate the controllability and observability properties of a family of linear dynamical systems whose structure is induced by the laplacian of a grid graph this analysis is motivated by several applications in network control and estimation quantum computation and discretization of partial differential equations specifically we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph for each eigenvalue based on its multiplicity and on suitable symmetries of the corresponding eigenvectors we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable observable we discuss the proposed criteria and show through suitable examples how such criteria reduce the complexity of the controllability respectively observability analysis of the grid

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

a characterization of optimal designs for observational studies summary an empirical investigation of the effects of a treatment is an observational study if it involves the comparison of treated and control groups that were not formed by randomization in such studies treated and control groups may differ systematically with respect to pretreatment measures or covariates and addressing these pre treatment differences is a central concern matching and subclassification are two standard methods of adjusting for observed pretreatment differences they may be used alone e g cochran 1968 or in conjunction with analytical or model based adjustments e g rubin 1973 1979 holford 1978 rosenbaum and rubin 1984 section 3 3 and rosenbaum 1987 1988a in particular rubin s simulation studies suggest that model based adjustments applied to matched or subclassified samples are more robust than model based adjustments applied to unmatched samples the purpose of this paper is to identify the structure of an optimal subclassification i e one in which the treated and control subjects in the same subclass are on average as similar as possible with respect to observed covariates it turns out that this structure is simple and intuitive while adjustments may control imbalances in observed covariates they cannot

adjustment uncertainty in effect estimation summary often there is substantial uncertainty in the selection of confounders when estimating the association between an exposure and health we define this type of uncertainty as adjustment uncertainty we propose a general statistical framework for handling adjustment uncertainty in exposure effect estimation for a large number of confounders we describe a specific implemen tation and we develop associated visualization tools theoretical results and simulation studies show that the proposed method provides consistent estimators of the exposure effect and its variance we also show that when the goal is to estimate an exposure effect accounting for ad justment uncertainty bayesian model averaging with posterior model probabilities approximated using information criteria can fail to estimate the exposure effect and can over or underestimate its variance we compare our approach to bayesian model averaging using time series data on levels of fine particulate matter and mortality

asymptotic separability in sensitivity analysis summary in an observational study in which each treated subject is matched to several untreated controls by using observed pretreatment covariates a sensitivity analysis asks how hidden biases due to unobserved covariates might alter the conclusions the bounds required for a sensitivity analysis are the solution to an optimization problem in general this optimization problem is not separable in the sense that one cannot find the needed optimum by performing a separate optimization in each matched set and combining the results we show however that this optimization problem is asymptotically separable so that when there are many matched sets a separate optimization may be performed in each matched set and the results combined to yield the correct optimum with negligible error this is true when the wilcoxon rank sum test or the hodgeslehmann aligned rank test is applied in matching with multiple controls numerical calculations show that the asymptotic approximation performs well with as few as 10 matched sets in the case of the rank sum test a table is given containing the separable solution with this table only simple arithmetic is required to conduct the sensitivity analysis the method also supplies estimates such as the hodges lehmann estimate and confidence intervals associated with rank tests the method is illustrated in a study of dropping out of us high schools and the effects on cognitive test scores

on the reachability and observability of path and cycle graphs in this technical note we investigate the reachability and observability properties of a network system running a laplacian based average consensus algorithm when the communication graph is a path or a cycle specifically we provide necessary and sufficient conditions based on simple rules from number theory to characterize all and only the nodes from which the network system is reachable respectively observable interesting immediate corollaries of our results are i a path graph is reachable observable from any single node if and only if the number of nodes of the graph is a power of two n 2i i n and ii a cycle is reachable observable from any pair of nodes if and only if n is a prime number for any set of control observation nodes we provide a closed form expression for the unreachable unobservable eigenvalues and for the eigenvectors of the unreachable unobservable subsystem

interval estimation for treatment effects using propensity score matching in causal studies without random assignment of treatment causal effects can be estimated using matched treated and control samples where matches are obtained using estimated propensity scores propensity score matching can reduce bias in treatment effect estimators in cases where the matched samples have overlapping covariate distributions despite its application in many applied problems there is no universally employed approach to interval estimation when using propensity score matching in this article we present and evaluate approaches to interval estimation when using propensity score matching

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

calibration estimators in survey sampling abstract this article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information estimation is equivalent to attaching weights to the survey data we focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations we briefly mention an application to the case in which the information consists of known marginal counts in a two or multi way table known as generalized raking the general regression estimator greg was conceived with multivariate auxiliary information in mind ordinarily this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x but we note that the greg can be derived by a different route by focusing instead on the weights the ordinary sampling weights of the kth observation is 1 k where k is the inclusion probabilit

optimal asymptotic bounds for spherical designs in this paper we prove the conjecture of korevaar and meyers for each n cdt d there exists a spherical t design in the sphere s d consisting of n points where cd is a constant depending only on d

joint sufficient dimension reduction and estimation of conditional and average treatment effects the estimation of treatment effects based on observational data usually involves multiple confounders and dimension reduction is often desirable and sometimes inevitable we first clarify the definition of a central subspace that is relevant for the efficient estimation of average treatment effects a criterion is then proposed to simultaneously estimate the structural dimension the basis matrix of the joint central subspace and the optimal bandwidth for estimating the conditional treatment effects the method can easily be implemented by forward selection semiparametric efficient estimation of average treatment effects can be achieved by averaging the conditional treatment effects with a different data adaptive bandwidth to ensure optimal undersmoothing asymptotic properties of the estimated joint central subspace and the corresponding estimator of average treatment effects are studied the proposed methods are applied to a nutritional study where the covariate dimension is reduced from 11 to an effective dimension of one

generalized raking procedures in survey sampling abstract we propose the name generalized raking for the class of procedures developed in this article because the classical raking ratio of w e deming is a special case generalized raking can be used for estimation in surveys with auxiliary information in the form of known marginal counts in a frequency table in two or more dimensions an important property of the generalized raking weights is that they reproduce the known marginal counts when applied to the categorical variables that define the frequency table our starting point is a class of distance measures and a set of original weights in the form of the standard sampling weights 1 k where k is the inclusion probability of element k new weights are derived by minimizing the total distance between original weights and new weights the article makes contributions in three areas 1 statistical inference conditionally on estimated cell counts 2 simple calculation of variance estimates for the generalized raking estimators and 3 presen

zero forcing number constrained matchings and strong structural controllability abstract the zero forcing number is a graph invariant introduced to study the minimum rank of the graph in 2008 aazami proved the np hardness of computing the zero forcing number of a simple undirected graph we complete this np hardness result by showing that the non equivalent problem of computing the zero forcing number of a directed graph allowing loops is also np hard the rest of the paper is devoted to the strong controllability of a networked system this kind of controllability takes into account only the structure of the interconnection graph but not the interconnection strengths along the edges we provide a necessary and sufficient condition in terms of zero forcing sets for the strong controllability of a system whose underlying graph is a directed graph allowing loops moreover we explain how our result differs from a recent related result discovered by monshizadeh et al finally we show how to solve the problem of finding efficiently a minimum size input set for the strong controllability of a self damped system with a tree structure

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

information theoretic approaches to inference in moment condition models one step efficient gmm estimation has been developed in the recent papers of back and brown 1990 imbens 1993 and qin and lawless 1994 these papers emphasized methods that correspond to using owen s 1988 method of empirical likelihood to reweight the data so that the reweighted sample obeys all the moment restrictions at the parameter estimates in this paper we consider an alternative klic motivated weighting and show how it and similar discrete reweightings define a class of unconstrained optimization problems which includes gmm as a special case such klic motivated reweightings introduce m auxiliary tilting parameters where m is the number of moments parameter and overidentification hypotheses can be recast in terms of these tilting parameters such tests when appropriately conditioned on the estimates of the original parameters are often startlingly more effective than their conventional counterparts this is apparently due to the local ancillarity of the original parameters for the tilting parameters

controllability improvement for multi agent systems leader selection and weight adjustment abstractfor an uncontrollable system adding leaders and adjusting edge weights are two methods to improve controllability in this paper the controllability of multi agent systems under directed topologies is studied especially on the leader selection problem and the weight adjustment problem for a multi agent system necessary and sufficient algebraic conditions for controllability with fewest leaders are proposed to improve controllability by adjusting edge weights the system is supposed to be structurally controllable which holds if and only if the communication topology contains a spanning tree it is also proved that the number of the fewest edges needed to be assigned on new weights equals the rank deficiency of controllability matrix in addition a leader selection algorithm and a weight adjustment algorithm are presented simulation examples are provided to illustrate the theoretical results

on the role of the propensity score in efficient semiparametric estimation of average treatment effects in this paper the role of the propensity score in the efficient estimation of average treatment effects is examined under the assumption that the treatment is ignorable given some observed characteristics it is shown that the propensity score is ancillary for estimation of the average treatment effects the propensity score is not ancillary for estimation of average treatment effects on the treated it is suggested that the marginal value of the propensity score lies entirely in the dimension reduction efficient semiparametric estimators of average treatment effects and average treatment effects on the treated are shown to take the form of relevant sample averages of the data completed by the nonparametric imputation method it is shown that the projection on the propensity score is not necessary for efficient semiparametric estimation of average treatment effects on the treated even if the propensity score is known an application to the experimental data reveals that conditioning on the propensity score may even result in a loss of efficiency

optimal matching for observational studies abstract matching is a common method of adjustment in observational studies currently matched samples are constructed using greedy heuristics or stepwise procedures that produce in general suboptimal matchings with respect to a particular criterion a matched sample is suboptimal if it could be improved by changing the controls assigned to specific treated units that is if it could be improved with the data at hand here optimal matched samples are obtained using network flow theory in addition to providing optimal matched pair samples this approach yields optimal constructions for several statistical matching problems that have not been studied previously including the construction of matched samples with multiple controls with a variable number of controls and the construction of balanced matched samples that combine features of pair matching and frequency matching computational efficiency is discussed extensive use is made of ideas from two essentially disjoint literatures namely st

multiply robust estimation of causal quantile treatment effects in causal inference often the interest lies in the estimation of the average causal effect other quantities such as the quantile treatment effect may be of interest as well in this article we propose a multiply robust method for estimating the marginal quantiles of potential outcomes by achieving mean balance in a the propensity score and b the conditional distributions of potential outcomes an empirical likelihood or entropy measure approach can be utilized for estimation instead of inverse probability weighting which is known to be sensitive to the misspecification of the propensity score model simulation studies are conducted across different scenarios of correctness in both the propensity score models and the outcome models both simulation results and theoretical development indicate that our proposed estimator is consistent if any of the models are correctly specified in the data analysis we investigate the quantile treatment effect of mothers smoking status on infants birthweight

model based direct adjustment abstract direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population direct adjustment has several attractive features but when there are many subclasses it can attach large weights to small quantities of data often in a fairly erratic manner in the extreme direct adjustment can attach infinite weight to nonexistent data a noticeable inconvenience in practice this article proposes a method of model based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses the sample mean and conventional direct adjustment are both special cases of model based direct adjustment under two different extreme models for the subclass specific selection probabilities the discussion of this method provides some insights into the behavior of true and estimated propensity scores the estimated scores

graph controllability classes for the laplacian leader follower dynamics in this paper we consider the problem of obtaining graph theoretic characterizations of controllability for the laplacian based leader follower dynamics our developments rely on the notion of graph controllability classes namely the classes of essentially controllable completely uncontrollable and conditionally controllable graphs in addition to the topology of the underlying graph the controllability classes rely on the specification of the control vectors our particular focus is on the set of binary control vectors the choice of binary control vectors is naturally adapted to the laplacian dynamics as it captures the case when the controller is unable to distinguish between the followers and moreover controllability properties are invariant under binary complements we prove that the class of essentially controllable graphs is a strict subset of the class of asymmetric graphs and provide numerical results that suggests that the ratio of essentially controllable graphs to asymmetric graphs increases as the number of vertices increases although graph symmetries play an important role in graph theoretic characterizations of controllability we provide an explicit class of asymmetric graphs that are completely uncontrollable namely the class of block graphs of steiner triple systems we prove that for graphs on four and five vertices a repeated laplacian eigenvalue is a necessary condition for complete uncontrollability but however show through explicit examples that for eight and nine vertices a repeated eigenvalue is not necessary for complete uncontrollability for the case of conditional controllability we give an easily checkable necessary condition that identifies a class of binary control vectors that result in a two dimensional controllable subspace several constructive examples demonstrate our results

estimation with missing data beyond double robustness summary we propose an estimator that is more robust than doubly robust estimators based on weighting completecasesusingweightsotherthaninverseprobabilitywhenestimatingthepopulationmean of a response variable subject to ignorable missingness we allow multiple models for both the propensity score and the outcome regression our estimator is consistent if any of the multiple models is correctly specified such multiple robustness against model misspecification is a significant improvement over double robustness which allows only one propensity score model and one outcome regression model our estimator attains the semiparametric efficiency bound when one propensity score model and one outcome regression model are correctly specified without requiring knowledge of which models are correct

controllability of multi agent systems with directed and weighted signed networks abstract this paper studies the controllability of multi agent systems with signed networks which are represented by directed weighted signed graphs the adjacency weights of network depict the property of interactions positive weight means cooperative interaction while negative weight antagonistic interaction first by using switching equivalent transformation the controllability of three kinds of signed networks is studied structurally balanced anti balanced and strictly unbalanced it is shown that the controllability of the structurally balanced network is equivalent to that of the associated underlying network then a graph theoretic necessary condition for controllability is given by virtue of almost equitable partition of directed weighted signed networks furthermore some necessary and sufficient conditions are given for the controllability of generic linear multi agent systems in addition several examples are presented to illustrate the theoretical results

nonparametric maximum likelihood estimation by the method of sieves maximum likelihood estimation often fails when the parameter takes values in an infinite dimensional space for example the maximum likelihood method cannot be applied to the completely nonparametric estimation of a density function from an operatorname iid sample the maximum of the likelihood is not attained by any density in this example as in many other examples the parameter space positive functions with area one is too big but the likelihood method can often be salvaged if we first maximize over a constrained subspace of the parameter space and then relax the constraint as the sample size grows this is grenander s method of sieves application of the method sometimes leads to new estimators for familiar problems or to a new motivation for an already well studied technique we will establish some general consistency results for the method and then we will focus on three applications

doubly robust estimation in missing data and causal inference models the goal of this article is to construct doubly robust dr estimators in ignorable missing data and causal inference models in a missing data model an estimator is dr if it remains consistent when either but not necessarily both a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified because with observational data one can never be sure that either a missingness model or a complete data model is correct perhaps the best that can be hoped for is to find a dr estimator dr estimators in contrast to standard likelihood based or nonaugmented inverse probability weighted estimators give the analyst two chances instead of only one to make a valid inference in a causal inference model an estimator is dr if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct inference based on dr estimators should improve upon previous approaches indeed we present the results of simulation studies which demonstrate that the finite sample performance of dr estimators is as impressive as theory would predict the proposed method is applied to a cardiovascular clinical trial

effect modification and design sensitivity in observational studies in an observational study of treatment effects subjects are not randomly assigned to treatment or control so differing outcomes in treated and control groups may reflect a bias from nonrandom assignment rather than a treatment effect after adjusting for measured pretreatment covariates perhaps by matching a sensitivity analysis determines the magnitude of bias from an unmeasured covariate that would need to be present to alter the conclusions of the naive analysis that presumes adjustments eliminated all bias other things being equal larger effects tend to be less sensitive to bias than smaller effects effect modification is an interaction between a treatment and a pretreatment covariate controlled by matching so that the treatment effect is larger at some values of the covariate than at others in the presence of effect modification it is possible that results are less sensitive to bias in subgroups experiencing larger effects two cases are considered i an a priori grouping into a few categ

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

protocols design and uncontrollable topologies construction for multi agent networks this note investigates the controllability issues of multi agent systems where each node contains generic linear dynamics first a neighbor based control protocol is proposed under which it is shown that the controllability of a multi agent system is solely decided by its communication topology structure we then further consider the effects of communication topology on the controllability from a graph theory point of view by explicitly constructing topologies the construction exhibits a partition of the designed graph with identified leaders under which the system is shown to be uncontrollable

empirical likelihood based inference in missing response problems and its application in observational studies summary the problem of missing response data is ubiquitous in medical and social science studies in the case of responses that are missing at random depending on some covariate information analyses focused only on the complete data may lead to biased results various debias methods have been extensively studied in the literature particularly the weighting method that was motivated by horvitz and thompson s estimators to improve efficiency robins rotnitzky and zhao proposed augmented estimating equations based on corrected complete case analyses a nice feature of the augmented method is its double robustness i e the estimator that is derived from the augmented method is asymptotically unbiased if either the underlying missing data mechanism or the underlying regression function is correctly specified furthermore the augmented estimator can achieve full efficiency if both the missing data mechanism and the regression function are correctly specified in general however it is very difficult to specify the regression function correctly especially when the dimension of covariates is high this is the so called curse of dimensionality problem the augmented estimator has much lower efficiency if the working regression model is not close to the true regression model in this paper the empirical likelihood method is employed to seek a constrained empirical likelihood estimation of mean response with the assumption that responses are missing at random the empirical likelihood based estimators enjoy the double robustness property moreover it is possible that the empirical likelihood based inference can produce asymptotically unbiased and efficient estimators even if the true regression function is not completely known simulation results indicate that the empirical likelihood based estimators are very robust to a misspecification of the propensity score and dominate other competitors in the sense of having smaller mean square errors methods that are developed in this paper have a nice application in observational causal inferences the propensity score is used to adjust for differences in pretreatment variables in the estimation of average treatment effects

mann whitney test with adjustments to pretreatment variables for missing values and observational study the conventional wilcoxon mann whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies this is because the missingness of the outcomes or the participation in the treatments may depend on certain pre treatment variables we propose an approach to adjust the mann whitney test by correcting the potential bias via consistently estimating the conditional distributions of the outcomes given the pre treatment variables we also propose semiparametric extensions of the adjusted mann whitney test which leads to dimension reduction for high dimensional covariate a novel bootstrap procedure is devised to approximate the null distribution of the test statistics for practical implementations results from simulation studies and an economic observational study data analysis are presented to demonstrate the performance of the proposed approach