a semiparametric extension of the mann whitney test for randomly truncated data in many applications statistical data are frequently observed subject to a retrospective sampling criterion resulting in pure right truncated data in classical testing problems the mann whitney test is used for testing the equality of two distributions a semiparametric extension of this test is developed for the case when truncation is present we consider a model in which the truncation distribution is parameterized while the lifetime distribution is left as a nonparametric component the method is seen to be applicable to many patterns of truncation including left truncation right truncation and doubly truncated data for which no other nonparametric or semiparametric test is currently available applications of the semiparametric method are given simulation results indicate that for pure right truncated data the semiparametric test is more powerful than a recent nonparametric test

recognition of spatial point patterns abstract complex patterns may sometimes be efficiently represented by a small number of points extracted from the image on the basis of atypical properties of neighborhoods of the points in this paper we describe theoretical and experimental results on the use of sequences of interpoint distances extracted from a noisy point image to match the image with one of a set of prototypes minimal spanning tree and nearest neighbor distances are used for these computations the methods applied are invariant under translation and rotation of the image and could be made invariant to scale changes several distance measures between classes are defined sufficient conditions for the separability of classes are given in terms of these measures

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

associative dynamic programs abstract in this paper we consider finite stage stochastic dynamic programs with associative reward systems an invariant imbedding technique yields a dynamic program with a terminal reward system on an augmented state space according to the associativity we clarify the validity of three possible recursive equations one parametrized equation and two non parametrized ones each of the additive multiplicative and multiplicative additive dynamic programs admits the three recursive equations further the corresponding composite relations among three optimum value functions hold however minimum maximum and fractional dynamic programs admit only the parametrized recursive equation they do not admit the two non parametrized equations further the corresponding relations among the three optimum value functions do not hold

nonparametric regression estimates using misclassified binary responses summary for random design nonparametric regression in the case that the responses are binary and subject to misclassification the performance of the kernel estimator is investigated the kernel estimator is generally biased for the local proportion to adjust for the bias the double sampling scheme of tenenbein 1970 1971 is considered a plugged in kernel estimator and an imputed kernel estimator which adjust for the effect of misclassification on the kernel estimator are proposed and their asymptotic mean squared errors are analysed the plugged in kernel estimator is better than the simple kernel estimator which uses only the data without misclassification in the validation subsample in the sense of having smaller asymptotic mean squared error however the imputed kernel estimator has smaller asymptotic variance if the misclassification probabilities are constant then the two proposed estimators have the same asymptotic bias in this case the imputed kernel estimator is always better than the plugged in kernel estimator for general misclassification probabilities the asymptotic biases of the two proposed estimators are not comparable in magnitude however our simulation results demonstrate that even when the misclassification probabilities are not constant the imputed kernel estimator is still better for reasonable sample sizes

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

conditional decision processes with recursive function we consider stochastic optimization of not necessarily additive but recursive functions over multistage decision processes without assuming any monotonicity we optimize a regular process by a direct dynamic programming approach on the regular decision process we propose two related conditional decision processes an a posteriori conditional decision process and an a priori when the markov transition law degenerates into a deterministic dynamics the two conditional processes reduce to the same deterministic decision process the conditional processes with monotonicity are optimized by the usual backward dynamic programming we show that under additional convexity the regular process dominates the a priori in maximum value function and the a priori does the a posteriori we show that the a posteriori process illustrates kreps and porteus s dynamic choice problem the numerical example also verifies the dominance relation in three optimal value functions

increasing the power of the mann whitney test in randomized experiments through flexible covariate adjustment the mann whitney u test is frequently used to evaluate treatment effects in randomized experiments with skewed outcome distributions or small sample sizes it may lack power however because it ignores the auxiliary baseline covariate information that is routinely collected wald and score tests in so called probabilistic index models generalize the mann whitney u test to enable adjustment for covariates but these may lack robustness by demanding correct model specification and do not lend themselves to small sample inference using semiparametric efficiency theory we here propose an alternative extension of the mann whitney u test which increases its power by exploiting covariate information in an objective way and which lends itself to permutation inference simulation studies and an application to an hiv clinical trial show that the proposed permutation test attains the nominal type i error rate and can be drastically more powerful than the classical mann whitney u test copyright 2014 john wiley sons ltd

approximating maximum clique with a hopfield network in a graph a clique is a set of vertices such that every pair is connected by an edge max clique is the optimization problem of finding the largest clique in a given graph and is np hard even to approximate well several real world and theory problems can be modeled as max clique in this paper we efficiently approximate max clique in a special case of the hopfield network whose stable states are maximal cliques we present several energy descent optimizing dynamics both discrete deterministic and stochastic and continuous one of these emulates as special cases two well known greedy algorithms for approximating max clique we report on detailed empirical comparisons on random graphs and on harder ones mean field annealing an efficient approximation to simulated annealing and a stochastic dynamics are the narrow but clear winners all dynamics approximate much better than one which emulates a naive greedy heuristic

approximating conditional distribution functions using dimension reduction motivated by applications to prediction and forecasting we sug gest methods for approximating the conditional distribution function of a random variable y given a dependent random d vector x the idea is to estimate not the distribution of y x but that of y t x where the unit vectoris selected so that the approximation is opti mal under a least squares criterion we show thatmay be estimated root n consistently furthermore estimation of the conditional distri bution function of y givent x has the same first order asymptotic properties that it would enjoy ifwere known the proposed method is illustrated using both simulated and real data examples showing its effectiveness for both independent datasets and data from time series numerical work corroborates the theoretical result thatcan be estimated particularly accurately

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

dot pattern processing using voronoi neighborhoods a sound notion of the neighborhood of a point is essential for analyzing dot patterns the past work in this direction has concentrated on identifying pairs of points that are neighbors examples of such methods include those based on a fixed radius k nearest neighbors minimal spanning tree relative neighborhood graph and the gabriel graph this correspondence considers the use of the region enclosed by a point s voronoi polygon as its neighborhood it is argued that the voronoi polygons possess intuitively appealing characteristics as would be expected from the neighborhood of a point geometrical characteristics of the voronoi neighborhood are used as features in dot pattern processing procedures for segmentation matching and perceptual border extraction using the voronoi neighborhood are outlined extensions of the voronoi definition to other domains are discussed

matching delaunay graphs this paper describes a bayesian framework for matching delaunay triangulations relational structures of this sort are ubiquitous in intermediate level computer vision being used to represent both voronoi tessellations of the image plane and volumetric surface data our matching process is realised in terms of probabilistic relaxation the novelty of our method stems from its use of a support function specified in terms of face units of the graphs under match in this way we draw on more expressive constraints than is possible at the level of edge units alone in order to apply this new relaxation process to the matching of realistic imagery requires a model of the compatibility between faces of the data and model graphs we present a particularly simple compatibility model that is entirely devoid of free parameters it requires only knowledge of the numbers of nodes edges and faces in the model graph the resulting matching scheme is evaluated on radar images and compared with its edge based counterpart we establish the operational limits and noise sensitivity on the matching of random dot patterns

a kernel method for estimating finite population distribution functions using auxiliary information summary this paper considers the use of auxiliary information to improve the estimation of the distribution function of a finite population a method is proposed which combines the known distribution of the auxiliary variable with a kernel estimate of the conditional distribution of the survey variable given the value of the auxiliary variable the resulting estimator compares favourably with existing estimators in terms of efficiency conditional behaviour and robustness the proposed method also has the advantage of producing estimates which are bona fide distribution functions this is not the case for many calibration type estimators suggested in the literature finally the proposed method is applicable under any probability sampling scheme

exact two sample inference with missing data when comparing follow up measurements from two independent populations missing records may arise due to censoring by events whose occurrence is associated with baseline covariates in these situations inferences based only on the completely followed observations may be biased if the follow up measurements and the covariates are correlated this article describes exact inference for a class of modified u statistics under covariate dependent dropouts the method involves weighing each permutation according to the retention probabilities and thus requires estimation of the missing data mechanism the proposed procedure is nonparametric in that no distributional assumption is necessary for the outcome variables and the missingness patterns monte carlo approximation by the gibbs sampler is proposed and is shown to be fast and accurate via simulation the method is illustrated in two small data sets for which asymptotic inferential procedures may not be appropriate

fast algorithm for point pattern matching invariant to translations rotations and scale changes abstract based on 2 d cluster approach a fast algorithm for point pattern matching is proposed to effectively solve the problems of optimal matches between two point pattern under geometrical transformation and correctly identify the missing or spurious points of patterns theorems and algorithms are developed to determine the matching pairs support of each point pair and its transformation parameters scaling s and rotation on a two parameter space s experiments are conducted both on real and synthetic data the experimental results show that the proposed matching algorithm can handle translation rotation and scaling differences under noisy or distorted condition the computational time is just about 0 5 s for 50 to 50 point matching on sun 4 workstation

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

fuzzy dynamic programming main developments and applications abstract we survey major developments and applications of fuzzy dynamic programming which is here advocated as a promising attempt at making dynamic programming models more realistic by a relaxation of often artificial assumptions of precision as to the constraints goals states and their transitions termination time etc issues related to numerical efficiency are considered applications in r d planning health care and medicine socioeconomic regional development energy systems water and environmental systems chemical engineering etc are surveyed

cross validation and the estimation of conditional probability densities many practical problems especially some connected with forecasting require nonparametric estimation of conditional densities from mixed data for example given an explanatory data vector x for a prospective customer with components that could include the customer s salary occupation age sex marital status and address a company might wish to estimate the density of the expenditure y that could be made by that person basing the inference on observations of x y for previous clients choosing appropriate smoothing parameters for this problem can be tricky not in the least because plug in rules take a particularly complex form in the case of mixed data an obvious difficulty is that there exists no general formula for the optimal smoothing parameters more insidiously and more seriously it can be difficult to determine which components of x are relevant to the problem of conditional inference for example if the jth component of x is independent of y then that component is irrelevant to es

an optimistic decision making in fuzzy environment bellman and zadeh have originated three systems of multistage decision processes in a fuzzy environment deterministic stochastic and fuzzy systems in this article we consider an optimization problem with an optimistic criterion on a fuzzy system by making use of minimization maximization expectation in a fuzzy environment we derive a recursive equation for the fuzzy decision process through invariant imbedding approach by illustrating a three state two decision and two stage model we give an optimal solution through dynamic programming the optimal solution is also verified by the method of multistage fuzzy decision tree table

labeled point pattern matching by delaunay triangulation and maximal cliques abstract in many problems of pattern recognition objects in an image may be efficiently represented by a set of labeled points this paper describes a method for matching labeled point patterns with one of the prototypes the delaunay triangulation is used to partition a point pattern into a set of triangles and the largest maximal clique of the consistency graph for each triangle is used to obtain the largest set of mutually consistent point pairs the proposed method is invariant under affine transformation of point patterns and allows for additions and deletions of points and some random perturbations in their relative locations the method is applied to the matching of constellations

approximate geometric pattern matching under rigid motions we present techniques for matching point sets in two and three dimensions under rigid body transformations we prove bounds on the worst case performance of these algorithms to be within a small constant factor of optimal and conduct experiments to show that the average performance of these matching algorithms is often better than that predicted by the worst case bounds

stochastic optimization of forward recursive functions this note solves a finite horizon stochastic optimization problem with forward recursive criterion through dynamic programming the forward recursive criterion is wide it includes additive discounted multiplicative discounted risk sensitive minimum and terminal criteria the basic idea is to apply invariant imbedding method for the stochastic optimization the method incorporates recursive accumulation process into dynamics by expanding the original state space

spectra of shape contexts an application to symbol recognition the pixel level constraint plc histograms are known for robustness and invariance in symbol recognition but limited in o n 3 complexity this paper proves that matching two plc histograms can approximately be solved as matching the power spectra of the corresponding shape contexts as a result spectra of shape contexts ssc inherit robustness and invariance from plc while the computational cost can be reduced moreover a maximum clique based scheme is proposed for outlier rejection the theoretical and experimental validation justifies that ssc possesses the desired properties for symbol recognition that is robustness invariance and efficiency it outperforms plc in terms of robustness and time efficiency and shape context in terms of rotation invariance

matching hierarchical structures using association graphs it is well known that the problem of matching two relational structures can be posed as an equivalent problem of finding a maximal clique in a derived association graph however it is not clear how to apply this approach to computer vision problems where the graphs are hierarchically organized i e are trees since maximal cliques are not constrained to preserve the partial order we provide a solution to the problem of matching two trees by constructing the association graph using the graph theoretic concept of connectivity we prove that in the new formulation there is a one to one correspondence between maximal cliques and maximal subtree isomorphisms this allows us to cast the tree matching problem as an indefinite quadratic program using the motzkin straus theorem and we use replicator dynamical systems developed in theoretical biology to solve it such continuous solutions to discrete problems are attractive because they can motivate analog and biological implementations the framework is also extended to the matching of attributed trees by using weighted association graphs we illustrate the power of the approach by matching articulated and deformed shapes described by shock trees

graphical templates for model registration a new method of model registration is proposed using graphical templates a graph of landmarks is chosen in the template image all possible candidates for these landmarks are found in the data image using local operators a dynamic programming algorithm on decomposable subgraphs of the template graph finds the optimal match to a subset of the candidate points in polynomial time this combination of local operators to describe points of interest landmarks and a graph to describe their geometric orientation in the plane yields fast and precise matches of the model to the data with no initialization required

efficient and doubly robust imputation for covariate dependent missing responses in this article we study a well known response missing data problem missing data is an ubiquitous problem in medical and social science studies imputation is one of the most popular methods for dealing with missing data the most commonly used imputation that makes use of covariates is regression imputation in which the regression model can be parametric semiparametric or nonparametric parametric regression imputation is efficient but is not robust against misspecification of the regression model although nonparametric regression imputation such as nearest neighbor imputation and kernel regression imputation is model free it is not efficient especially if the dimension of covariate vector is high the well known problem of curse of dimensionality semiparametric regression imputation such as partially linear regression imputation can reduce the dimension of the covariate in nonparametric regression fitting but is not robust against misspecification of the linear component in the regression

sequential decision making in fuzzy environment in this paper we reexamine bellman and zadeh s seminal paper on multistage decision making in a fuzzy environment we propose a correction to their functional equation associated with a stochastic system and formulate a model for deterministic processes governed by fuzzy dynamics

dynamic programming for fuzzy systems with fuzzy environment abstract a dynamic programming functional equation for a multi stage decision problem with fuzzy dynamics and environment is formulated and solved by a process of fuzzy interpolation this is an extension of the bellman zadeh model

use of regression functions for improved estimation of means summary suppose one has a random sample from a distribution fy x the goal being to estimate u4 the unconditional mean of y if the regression function of y on x is of a known parametric form one might consider estimating u by the average of the estimated regression function values at the sample points it is shown here that such an estimator can offer substantial improvement over the sample mean of y and that in no case does the former estimator have larger asymptotic variance than the latter estimator applications of this asymptotic distribution theory to the double sampling setting are also given

labeled point pattern matching by fuzzy relaxation abstract a method of matching labeled point patterns is described on the basis of a fuzzy relaxation the method is applicable to labeled point patterns which differ by geometrical transformations such as translation rotation and scale change in this method the point pairs are considered to be the pattern primitives the pattern primitives are geometrically transformed in the process of relaxation so as to minimize a measure of mismatch between the primitive pairs the compatible primitive pairs between the two labeled point patterns are established after only a few iterations of relaxation and the corresponding points are obtained from the primitive pairs as an example the method is applied to the matching of constellations

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

a class of dual fuzzy dynamic programs in this paper we propose a large class of fuzzy dynamic programs by use of the notion of dual binary relation we define a dual fuzzy dynamic program in the class we establish two duality theorems between primal and dual fuzzy dynamic programs one is for the two parametric recursive equations the other is for the nonparametric we specify maximum minimum process and minimum minimum process in fuzzy environment and multiplicative multiplicative process in quasi stochastic environment it is shown that the duality theorems hold between primal and dual programs

local linear regression for generalized linear models with missing data fan heckman and wand proposed locally weighted kernel polynomial regression methods for generalized linear models and quasilikelihood functions when the covariate variables are missing at random we propose a weighted estimator based on the inverse selection probability weights distribution theory is derived when the selection probabilities are estimated nonparametrically we show that the asymptotic variance of the resulting nonparametric estimator of the mean function in the main regression model is the same as that when the selection probabilities are known while the biases are generally different this is different from results in parametric problems where it is known that estimating weights actually decreases asymptotic variance to reconcile the difference between the parametric and nonparametric problems we obtain a second order variance result for the nonparametric case we generalize this result to local estimating equations finite sample performance is examined via simulation studies the proposed method is demonstrated via an analysis of data from a case control study

point matching using asymmetric neural networks abstract matching control points is an important step in many pattern recognition applications the matching problem is formulated under translation and rotation as a 0 1 integer programming problem and an artificial neural network is proposed for approximately solving it the solution to the 0 1 integer programming problem is obtained as the high gain limit point of the continuous network the network is capable of handling distortion and noise and can use both interpoint distance information and feature properties associated with the points the results obtained by the network compare favourably with that of the relaxation method of ton and jain ieee trans geosci remote sensing 27 642 651 1989

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

semiparametric dimension reduction estimation for mean response with missing data model misspecification can be a concern for high dimensional data nonparametric regression obviates model specification but is impeded by the curse of dimensionality this paper focuses on the estimation of the marginal mean response when there is missingness in the response and multiple covariates are available we propose estimating the mean response through nonparametric functional estimation where the dimension is reduced by a parametric working index the proposed semiparametric estimator is robust to model misspecification it is consistent for any working index if the missing mechanism of the response is known or correctly specified up to unknown parameters even with misspecification in the missing mechanism it is consistent so long as the working index can recover e y x the conditional mean response given the covariates in addition when the missing mechanism is correctly specified the semiparametric estimator attains the optimal efficiency if e y x is recoverable through the working index robustness and efficiency of the proposed estimator is further investigated by simulations we apply the proposed method to a clinical trial for hiv