direct estimation of the mean outcome on treatment when treatment assignment and discontinuation compete several authors have investigated the challenges of statistical analyses and inference in the presence of early treatment termination including a loss of efficiency in randomized controlled trials and a connection to dynamic regimes in observational studies popular estimation strategies for causal estimands in dynamic regimes lend themselves to studies where treatment is assigned at a finite number of points and the extension to continuous treatment assignment is nontrivial we re examine this from a different perspective and propose a new estimator for the mean outcome of a target treatment length policy that does not involve a treatment model because this strategy avoids modelling the treatment assignment mechanism the estimator works for both discrete and continuous treatment length data and eschews bias and imprecision that arise as a result of coarsening continuous time data into intervals we show how the competition of treatment length assignment and terminating event lead to a competing risks problem we exemplify the direct estimator through numerical studies and the analysis of two real datasets when all modelling assumptions for both the direct and inverse weighted estimators are correct our simulation studies suggest that the direct estimator is more precise

partially linear models with missing response variables and error prone covariates we consider partially linear models of the form y x t beta nu z epsilon when the response variable y is sometimes missing with missingness probability pi depending on x z and the covariate x is measured with error where nu z is an unspecified smooth function the missingness structure is therefore missing not at random rather than the usual missing at random we propose a class of semiparametric estimators for the parameter of interest beta as well as for the population mean e y the resulting estimators are shown to be consistent and asymptotically normal under general assumptions to construct a confidence region for beta we also propose an empirical likelihood based statistic which is shown to have a chi squared distribution asymptotically the proposed methods are applied to an aids clinical trial dataset a simulation study is also reported

equipercentile equating via data imputation techniques in the design of common item equating two groups of examinees are administered separate test forms and each test form contains a common subset of items we consider test equating under this situation as an incomplete data problem that is examinees have observed scores on one test form and missing scores on the other through the use of statistical data imputation techniques the missing scores can be replaced by reasonable estimates and consequently the forms may be directly equated as if both forms were administered to both groups in this paper we discuss different data imputation techniques that are useful for equipercentile equating we also use empirical data to evaluate the accuracy of these techniques as compared with chained equipercentile equating

a note on multiple imputation for method of moments estimation multiple imputation is a popular imputation method for general purpose estimation rubin 1987 provided an easily applicable formula for the variance estimation of multiple imputation however the validity of the multiple imputation inference requires the congeniality condition of meng 1994 which is not necessarily satisfied for method of moments estimation this paper presents the asymptotic bias of rubin s variance estimator when the method of moments estimator is used as a complete sample estimator in the multiple imputation procedure a new variance estimator based on over imputation is proposed to provide asymptotically valid inference for method of moments estimation

local multiple imputation dealing with missing data via parametric multiple imputation methods usually implies stating several strong assumptions both about the distribution of the data and about underlying regression relationships if such parametric assumptions do not hold the multiply imputed data are not appropriate and might produce inconsistent estimators and thus misleading results in this paper a fully nonparametric and a semiparametric imputation method are studied both based on local resampling principles it is shown that the final estimator based on these local imputations is consistent under fewer or no parametric assumptions asymptotic expressions for bias variance and mean squared error are derived showing the theoretical impact of the different smoothing parameters simulations illustrate the usefulness and applicability of the method

iterative algorithm of solutions for generalized mixed implicit equilibrium like problems in this paper we introduce a new class of generalized mixed implicit equilibrium like equilibrium problems gmielp by using auxiliary principle technique some new predictor corrector iterative algorithms for solving generalized mixed implicit equilibrium like problems are suggested and analyzed the convergence of the suggested methods only requires the continuity and the partially relaxed email protected monotonicity of mappings

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

nonparametric comparison of several regression functions exact and asymptotic theory a new test is proposed for the comparison of two regression curves f and g we prove an asymptotic normal law under fixed alternatives which can be applied for power calculations for constructing confidence regions and for testing precise hypotheses of a weighted l 2 distance between f and g in particular the problem of nonequal sample sizes is treated which is related to a peculiar formula of the area between two step functions these results are extended in various directions such as the comparison of k regression functions or the optimal allocation of the sample sizes when the total sample size is fixed the proposed pivot statistic is not based on a nonparametric estimator of the regression curves and therefore does not require the specification of any smoothing parameter

on difference based variance estimation in nonparametric regression when the covariate is high dimensional summary we consider the problem of estimating the noise variance in homoscedastic nonparametric regression models for low dimensional covariates t d d 1 2 difference based estimators have been investigated in a series of papers for a given length of such an estimator difference schemes which minimize the asymptotic mean squared error can be computed for d 1 and d 2 however from numerical studies it is known that for finite sample sizes the performance of these estimators may be deficient owing to a large finite sample bias we provide theoretical support for these findings in particular we show that with increasing dimension d this becomes more drastic if d4 these estimators even fail to be consistent a different class of estimators is discussed which allow better control of the bias and remain consistent when d4 these estimators are compared numerically with kernel type estimators which are asymptotically efficient and some guidance is given about when their use becomes necessary

the estimation of residual variance in nonparametric regression summary a wide class of estimators of the residual variance in nonparametric regression is considered namely those that are quadratic in the data unbiased for linear regression and always nonnegative the minimax mean squared error estimator over a natural class of regression functions is derived this optimal estimator has an interesting structure and is closely related to a minimax estimator of the regression curve itself

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

new classes of analytic solutions of the two level problem a simple technique to find analytic solutions of the time dependent schrodinger equations is introduced a number of three parametric classes of the two level problem integrable in terms of the gauss hypergeometric function including all presently known analytically solvable models are derived

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

nonparametric estimation of residual variance revisited summary several difference based estimators of residual variance are compared for finite sample size since the introduction of a rather simple estimator by gasser sroka jennensteinmetz 1986 other proposals have been made here the one given by hall kay titterington 1990 is of particular interest it minimizes the asymptotic variance unfortunately it has severe problems with finite sample bias and the estimator of gasser et al 1986 proves still to be a good choice a new estimator is introduced compromising between bias and variance

semiparametric regression analysis with missing response at random we develop inference tools in a semiparametric partially linear regression model with missing response data a class of estimators is defined that includes as special cases a semiparametric regression imputation estimator a marginal average estimator and a marginal propensity score weighted estimator we show that any of our class of estimators is asymptotically normal the three special estimators have the same asymptotic variance they achieve the semiparametric efficiency bound in the homoscedastic gaussian case we show that the jackknife method can be used to consistently estimate the asymptotic variance our model and estimators are defined with a view to avoid the curse of dimensionality which severely limits the applicability of existing methods the empirical likelihood method is developed it is shown that when missing responses are imputed using the semiparametric regression method the empirical log likelihood is asymptotically a scaled chi squared variable an adjusted empirical log likel

empirical likelihood for estimating equations with missing values we consider an empirical likelihood inference for parameters defined by general estimating equations when some components of the random observations are subject to missingness as the nature of the estimating equations is wide ranging we propose a nonparametric imputation of the missing values from a kernel estimator of the conditional distribution of the missing variable given the always observable variable the empirical likelihood is used to construct a profile likelihood for the parameter of interest we demonstrate that the proposed nonparametric imputation can remove the selection bias in the missingness and the empirical likelihood leads to more efficient parameter estimation the proposed method is further evaluated by simulation and an empirical study on a genetic dataset on recombinant inbred mice

data driven local bandwidth selection for additive models with missing data this paper deals in the nonparametric estimation of additive models in the presence of missing data in the response variable specifically in the case of additive models estimated by the backfitting algorithm with local polynomial smoothers 1 three estimators are presented one based on the available data and two based on a complete sample from imputation techniques we also develop a data driven local bandwidth selector based on a wild bootstrap approximation of the mean squared error of the estimators the performance of the estimators and the local bootstrap bandwidth selection method are explored through simulation experiments

empirical likelihood based difference in differences estimators summary recently there has been a surge in econometric and epidemiologic works focusing on estimating average treatment effects under various sets of assumptions estimation of average treatment effects in observational studies often requires adjustment for differences in pretreatment variables rosenbaum and rubin have proposed the propensity score method for estimating the average treatment effect by adjusting pretreatment variables in this paper the empirical likelihood method is used to estimate average treatment effects on the treated under the difference in differences framework the advantage of this approach is that the common marginal covariate information can be incorporated naturally to enhance the estimation of average treatment effects compared with other approaches in the literature the method proposed can provide more efficient estimation a simulation study and a real economic data analysis are presented

monitoring profiles based on nonparametric regression methods the use statistical process control spc in monitoring and diagnosis of process and product quality profiles remains an important problem in various manufacturing industries the spc problem with a nonlinear profile is particularly challenging this article proposes a novel scheme to monitor changes in both the regression relationship and the variation of the profile online it integrates the multivariate exponentially weighted moving average procedure with the generalized likelihood ratio test based on nonparametric regression the proposed scheme not only provides an effective spc solution to handle nonlinear profiles which are common in industrial practice but it also resolves the latent problem in popular parametric monitoring methods of being unable to detect certain types of changes due to a misspecified out of control model our simulation results demonstrate the effectiveness and efficiency of the proposed monitoring scheme in addition a systematic diagnostic approach is provided to locate t

a semiparametric estimation of mean functionals with nonignorable missing data parameter estimation with nonignorable missing data is a challenging problem in statistics the fully parametric approach for joint modeling of the response model and the population model can produce results that are quite sensitive to the failure of the assumed model we propose a more robust modeling approach by considering the model for the nonresponding part as an exponential tilting of the model for the responding part the exponential tilting model can be justified under the assumption that the response probability can be expressed as a semiparametric logistic regression model in this paper based on the exponential tilting model we propose a semiparametric estimation method of mean functionals with nonignorable missing data a semiparametric logistic regression model is assumed for the response probability and a nonparametric regression approach for missing data discussed in cheng 1994 is used in the estimator by adopting nonparametric components for the model the estimation method can be mad

conditional moment models with data missing at random summarywe consider a general statistical model defined by moment restrictions when data are missing at random using inverse probability weighting we show that such a model is equivalent to a model for the observed variables only augmented by a moment condition defined by the missingness mechanism our framework covers parametric and semiparametric mean regressions and quantile regressions we allow for missing responses missing covariates and any combination of them the equivalence result sheds new light on various aspects of missing data and provides guidelines for building efficient estimators

multivalued general equilibrium problems in this paper we use the auxiliary principle technique to suggest some new classes of iterative algorithms for solving multivalued equilibrium problems the convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity as special cases we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems since multivalued equilibrium problems include equilibrium variational inequality and complementarity problems as specials cases our results continue to hold for these problems

mixed equilibrium problems sensitivity analysis and algorithmic aspect abstract the aim of this paper is twofold first it is to extend the sensitivity analysis framework developed recently for variational inequalities to mixed equilibrium problems the second is to propose iterative methods for solving this kind of problems in the process we establish an equivalence between an extended version of wiener hopf equations and the given problems relying on a generalization of the yosida approximation notion our results generalize results obtained for optimization variational inequalities complementarity problems and problems of nash equilibria

a new class of analytic solutions of the two state problem a new class of solutions of the time dependent schrodinger equation is found for the two state problem often encountered in quantum optics magnetic resonance and atomic collisions the authors use the riemann papperitz differential equation to find exact solutions in terms of hypergeometric functions they consider only cases in which the final occupation probabilities are elementary functions of the parameters of the model

regression smoothing parameters that are not far from their optimum abstract it is well known that data driven regression smoothing parameters based on cross validation and related methods exhibit a slow rate of convergence to their optimum in an earlier article we showed that this rate can be as slow as n 1 10 that is for a bandwidth 0 optimizing the averaged squared error n 1 10 0 0 tends to an asymptotic normal distribution in this article we consider mean averaged squared error optimal bandwidths h 0 this nonrandom smoothing parameter can be approximated much faster we use the technique of double smoothing to show that there is an such that under certain conditions n 1 2 h 0 h 0 tends to an asymptotic normal distribution

semiparametric double balancing score estimation for incomplete data with ignorable missingness when estimating the marginal mean response with missing observations a critical issue is robustness to model misspecification in this article we propose a semiparametric estimation method with extended double robustness that attains the optimal efficiency under less stringent requirement for model specifications than the doubly robust estimators in this semiparametric estimation covariate information is collapsed into a two dimensional score s with one dimension for i the pattern of missingness and the other for ii the pattern of response both estimated from some working parametric models the mean response e y is then estimated by the sample mean of e y s which is estimated via nonparametric regression the semiparametric estimator is consistent if either the core of i or the core of ii is captured by s and attains the optimal efficiency if both are captured by s as the cores can be obtained without correctly specifying the full parametric models for i or ii the proposed es

estimation of mean response via the effective balancing score we introduce effective balancing scores for estimation of the mean response under a missing at random mechanism unlike conventional balancing scores the effective balancing scores are constructed via dimension reduction free of model specification three types of effective balancing scores are introduced those that carry the covariate information about the missingness the response or both they lead to consistent estimation with little or no loss in efficiency compared to existing estimators the effective balancing score based estimator relieves the burden of model specification and is the most robust it is a near automatic procedure which is most appealing when high dimensional covariates are involved we investigate both the asymptotic and the numerical properties and demonstrate the proposed method in a study on human immunodeficiency virus disease

fixed points and best proximity points in contractive cyclic self maps satisfying constraints in closed integral form with some applications this paper investigates the existence of best proximity points and the potential fixed points of p cyclic self maps which are defined on the union of a finite set of subsets of a certain uniform metric space under several integral type contractive conditions the corresponding properties of the associated restricted composed maps from any of the subsets to itself are also dealt with in a formal context the above subsets of the uniform metric space are not assumed to necessarily intersect but the case when they intersect leads to particular results of the general case in the sense that best proximity points become fixed points common fixed points and best proximity points of pairs of self maps on the above subsets of the uniform metric space are also investigated

existence and iterative approximation of solutions of generalized mixed equilibrium problems in this paper we consider a generalized mixed equilibrium problem involving non monotone set valued mappings in real hilbert space we extend the notions of the yosida approximation and its corresponding regularized operator given by moudafi and thera a moudafi m thera proximal and dynamical approaches to equilibrium problems in lecture notes in econom and math system vol 477 springer verlag berlin 2002 pp 187 201 and discuss some of their properties further we consider a generalized wiener hopf equation problem and show its equivalence with the generalized mixed equilibrium problem using a fixed point formulation of the generalized wiener hopf equation problem we construct an iterative algorithm furthermore we extend the notion of stability given by harder and hick a m harder t l hicks stability results for fixed point iteration procedures math japonica 33 5 1998 693 706 we prove the existence of a solution and discuss the convergence and stability of the iterative algorithm for the generalized wiener hopf equation problem since the generalized mixed equilibrium problems include variational inequalities as special cases the results presented in this paper continue to hold for these problems

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

nonparametric analysis of factorial designs with random missingness bivariate data we propose a nonparametric approach to the analysis of factorial designs where each subject is observed at two time points and both observations are subject to missingness the procedures are fully nonparametric in that they do not require continuity and do not impose models to describe the relation of the response distribution in different factor level combinations the approach for estimating and testing treatment and time effects is based on a method which we introduce for estimating a distribution function the method requires a pattern mixture type assumption on the missingness mechanism which is weaker than the missing completely at random assumption but neither weaker nor stronger than the missing at random assumption this missingness assumption is the minimal requirement for nonparametric analysis comparisons with normal based likelihood ratio tests indicate that the proposed tests fare well when the data are normal and homoscedastic and outperform them in many other cases simulations also

a flexible and fast method for automatic smoothing abstract the choice of smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators such as kernel estimators the optimal choice depends on the data at hand a data driven bandwidth selection close to the optimal one would make these curve estimators objective more reliable and easier to use minimizing residual mean squared error criteria such as cross validation have been frequently proposed to estimate the optimal smoothing parameter empirical and theoretical evidence indicates that cross validation rules and related methods lead to rather variable estimated optimal bandwidths the method presented here builds on estimating the asymptotically optimal bandwidth from the data since estimators for the residual variance and for an asymptotic expression for the bias are plugged into the asymptotic formula such selection rules are called plug in estimators the functional that quantifies bias is approximated by the integrated squared second derivative of the regre

a basic two state model for bosonic field theories with a cubic nonlinearity a basic nonlinear two state model generic in classical and bosonic field theories with a cubic nonlinearity is considered for the class of models with constant external field amplitude a general strategy for attacking the problem is developed based on the reduction of the initial system of equations for the semi classical atom molecule amplitudes to a nonlinear volterra integral equation for the molecular probability a uniformly convergent series solution to the problem is constructed for the weak interaction limit the landau zener model is considered as a specific example the first approximation term is derived and an asymptotic expression for the nonlinear transition probability is established in the weak interaction regime

estimation of heteroscedasticity in regression analysis consider the regression model y i g t i varepsilon i 1 leq i leq n with nonrandom design variables t i and measurements y i for the unknown regression function g cdot we assume that the data are heteroscedastic i e e varepsilon 2 i sigma 2 i not equiv operatorname const and investigate how to estimate sigma 2 i if sigma 2 i sigma 2 t i with a smooth function sigma 2 cdot initial estimators tilde sigma 2 i can be improved by kernel smoothers and the resulting class of estimators is shown to be uniformly consistent these estimates can be used to improve the estimation of the regression function g itself in parametric and nonparametric models further applications are suggested

predictor corrector algorithms for solving generalized mixed implicit quasi equilibrium problems a new class of generalized mixed implicit quasi equilibrium problems gmiqep with four functions is introduced and studied the new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi variational inequality problems as many special cases by employing the auxiliary principle technique some predictor corrector iterative algorithms for solving the gmiqep are suggested and analyzed the convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings

estimation in partially linear models with missing covariates the partially linear model y xt z has been studied extensively when data are completely observed in this article we consider the case where the covariate x is sometimes missing with missingness probability depending on y z new methods are developed for estimating and our methods are shown to outperform asymptotically methods based only on the complete data asymptotic efficiency is discussed and the semiparametric efficient score function is derived justification of the use of the nonparametric bootstrap in this context is sketched the proposed estimators are extended to a working independence analysis of longitudinal clustered data and applied to analyze an aids clinical trial dataset the results of a simulation experiment are also given to illustrate our approach

variance estimation in nonparametric regression via the difference sequence method consider a gaussian nonparametric regression problem having both an unknown mean function and unknown variance function this article presents a class of difference based kernel estimators for the variance function optimal convergence rates that are uniform over broad functional classes and bandwidths are fully characterized and asymptotic normality is also established we also show that for suitable asymptotic formulations our estimators achieve the minimax rate

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

analytic treatment of the polariton problem for a smooth interface we study the polariton problem for smooth boundaries i e whether or not there exist some localized solutions of maxwell s equations for different types of smooth spatial variation of complex dielectric and or magnetic permittivity tensors for a particular dielectric permittivity profile varying according to the hyperbolic tangent law the singular term is mathematically strongly taken into account in maxwell s equations not in the boundary conditions the problem is then reduced to the canonical form of heun s equation possessing four regular singular points the solution to heun s equation as a power series is constructed and an approximate solution involving a combination of two incomplete betafunctions is derived further the exact eigenvalue solution to the polariton problem as a series in terms of incomplete beta functions or equivalently gauss hypergeometric functions is constructed it is shown that the dispersion relation for the polariton wavenumber does not depend on the interface transition layer width i e it is always exactly the same as the one derived in the limit of abrupt interface we conjecture that the polariton wavenumber eigenvalue depends on either zeros of the dielectric permittivity variance profile or the poles of the logarithmic derivative of the latter

using a monotone single index model to stabilize the propensity score in missing data problems and causal inference the augmented inverse weighting method is one of the most popular methods for estimating the mean of the response in causal inference and missing data problems an important component of this method is the propensity score popular parametric models for the propensity score include the logistic probit and complementary log log models a common feature of these models is that the propensity score is a monotonic function of a linear combination of the explanatory variables to avoid the need to choose a model we model the propensity score via a semiparametric single index model in which the score is an unknown monotonic nondecreasing function of the given single index under this new model the augmented inverse weighting estimator aiwe of the mean of the response is asymptotically linear semiparametrically efficient and more robust than existing estimators moreover we have made a surprising observation the inverse probability weighting and aiwes based on a correctly specified parametric model may have worse performance than their counterparts based on a nonparametric model a heuristic explanation of this phenomenon is provided a real data example is used to illustrate the proposed methods

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

on variance estimation in nonparametric regression a simple explicit estimator of variance in nonparametric regression is suggested based on the mean square of a sequence of residuals the estimator is valid for general error distributions has elementary bias and variance properties and is optimal to both first and second orders

miscellanea combining parametric and empirical likelihoods imbens lancaster 1994 pointed out that census reports can be interpreted as providing nearly exact knowledge of moments of the marginal distribution of economic variables in this paper we show that empirical likelihood can effectively incorporate auxiliary information like this as long as it can be summarised as unbiased estimating equations by combining empirical and parametric likelihoods we show that the combined likelihood can produce valid inferences for the underlying parameters a wilks type theorem is proved for the combined likelihood ratio statistic simulation results demonstrate that the performance of the combined likelihood ratio confidence intervals is better than conventional confidence intervals that use a normal approximation

adaptive bandwidth choice for kernel regression abstract a data based procedure is introduced for local bandwidth selection for kernel estimation of a regression function at a point the estimated bandwidth is shown to be consistent and asymptotically normal as an estimator of the asymptotic optimal value for minimum mean square estimation simulation studies indicate satisfactory behavior of the new bandwidth estimator in finite samples the findings are improvements over a global bandwidth estimator the same methodology works for local linear regression and extends easily to weighted local polynomial fits

estimating equations inference with missing data there is a large and growing body of literature on estimating equation ee as an estimation approach one basic property of ee that has been universally adopted in practice is that of unbiasedness and there are deep conceptual reasons why unbiasedness is a desirable ee characteristic this article deals with inference from ees when data are missing at random the investigation is motivated by the observation that direct imputation of missing data in ees generally leads to ees that are biased and thus violates a basic assumption of the ee approach the main contribution of this article is that it goes beyond existing imputation methods and proposes a procedure whereby one mitigates the effects of missing data through a reformulation of ees imputed through a kernel regression method these modified ees then constitute a basis for inference by the generalized method of moments gmm and empirical likelihood el asymptotic properties of the gmm and el estimators of the unknown parameters are derived a

from multiple gaussian sequences to functional data and beyond a stein estimation approach summary we expand the notion of gaussian sequence models to n experiments and propose a stein estimation strategy which relies on pooling information across experiments an oracle inequality is established to assess conditional risks given the underlying effects based on which we can quantify the size of relative error and obtain a tuning free recovery strategy that is easy to compute produces model parsimony and extends to unknown variance we show that the simultaneous recovery is adaptive to an oracle strategy which also enjoys a robustness guarantee in a minimax sense a connection to functional data is established via le cam theory for fixed and random designs under general regularity settings we further extend the model projection to general bases with mild conditions on correlation structure and conclude with potential application to other statistical problems simulated and real data examples are provided to lend empirical support to the methodology proposed and to illustrate the potential for substantial computational savings

efficiency bounds for missing data models with semiparametric restrictions this paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random mar coincides with that of a particular augmented moment condition problem the augmented system consists of the inverse probability weighted ipw original moment restriction and an additional conditional moment restriction which exhausts all other implications of the mar assumption the paper also investigates the value of additional semiparametric restrictions on the conditional expectation function cef of the original moment function given always observed covariates in the program evaluation context for example such restrictions are implied by semiparametric models for the potential outcome cefs given baseline covariates the efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem some implications of these results for estimation are briefly discussed

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

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

nonparametric estimation in a regression model with additive and multiplicative noise abstract in this paper we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise we propose two new wavelet estimators in this general context we prove that they achieve fast convergence rates under the mean integrated square error over besov spaces the obtained rates have the particularity of being established under weak conditions on the model a numerical study in a context comparable to stochastic frontier estimation with the difference that the boundary is not necessarily a production function supports the theory

new classes of analytic solutions of the three state problem a rich multiparametric class of solutions of the time dependent schrodinger equations including many integrable cases known at present of the three state problem is derived in addition the class contains an infinite number of new multiparametric integrable subfamilies examples of such four parametric new subfamilies of asymmetric in general amplitude and frequency modulation functions permitting solution of the three state problem in terms of the clausen function are presented

handling estimating equation with nonignorably missing data based on sir algorithm abstract in this paper the estimation of parameters in estimating equation with nonignorably missing data is considered based on a logistic regression model for the response mechanism and an assumed parametric model for the distribution of respondents we propose to use the sampling importance resampling sir algorithm to calculate the conditional expectation for non respondents the proposed method can avoid the difficulty of high dimensional kernel smoothing on calculating the conditional expectation under nonignorably missing data based on the sir algorithm we derive a modified estimating equation to facilitate comparison we apply the empirical likelihood method to derive the parameters estimator some numerical simulation results based on linear and nonlinear models show that the proposed method is robust and performs the best among the compared existing methods so we extend the estimation method of e g y using sir algorithm with nonignorably missing response to the estimation of parameters in generalized estimating equation and obtain a new and more robust estimation method

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

the integrability of the two state problem in terms of confluent hypergeometric functions the reduction of the two state problem to the confluent hypergeometric equation via complex transformations of independent variables is considered it is shown that all the known analytically integrable cases can be generalized to a single formula a new class of integrable models of the two state problem in terms of confluent hypergeometric functions is presented

doubly robust type estimation for covariate adjustment in latent variable modeling due to the difficulty in achieving a random assignment a quasi experimental or observational study design is frequently used in the behavioral and social sciences if a nonrandom assignment depends on the covariates multiple group structural equation modeling that includes the regression function of the dependent variables on the covariates that determine the assignment can provide reasonable estimates under the condition of correct specification of the regression function however it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large therefore the propensity score adjustment methods have been proposed since they do not require the specification of the regression function and have been applied to several applied studies however these methods produce biased estimates if the assignment mechanism is incorrectly specified in order to make a more robust inference it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology in this study we propose a doubly robust type estimation method for marginal multiple group structural equation modeling this method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified a simulation study indicates that the proposed estimation method is more robust than the existing methods

asymptotically optimal difference based estimation of variance in nonparametric regression summary we define and compute asymptotically optimal difference sequences for estimating error variance in homoscedastic nonparametric regression our optimal difference sequences do not depend on unknowns such as the mean function and provide substantial improvements over the suboptimal sequences commonly used in practice for example in the case of normal data the usual variance estimator based on symmetric second order differences is only 64 efficient relative to the estimator based on optimal second order differences the efficiency of an optimal mth order difference estimator relative to the error sample variance is 2m 2m 1 again this is for normal data and increases as the tails of the error distribution become heavier

empirical likelihood based inference under imputation for missing response data inference under kernel regression imputation for missing response data is considered an adjusted empirical likelihood approach to inference for the mean of the response variable is developed a nonparametric version of wilks theorem is proved for the adjusted empirical log likelihood ratio by showing that it has an asymptotic standard chi squared distribution and the corresponding empirical likelihood confidence interval for the mean is constructed with auxiliary information an empirical likelihood based estimator is defined and an adjusted empirical log likelihood ratio is derived asymptotic normality of the estimator is proved also it is shown that the adjusted empirical log likelihood ratio obeys wilks theorem a simulation study is conducted to compare the adjusted empirical likelihood and the normal approximation methods in terms of coverage accuracies and average lengths of confidence intervals based on biases and standard errors a comparision is also made by simulation between the empirical likelihood based estimator and related estimators our simulation indicates that the adjusted empirical likelihood method performs competitively and that the use of auxiliary information provides improved inferences

iterative algorithm of solutions for a system of generalized mixed implicity equilibrium problems in reflexive banach spaces abstract in this paper a new system of generalized mixed implicity equilibrium problems involving non monotone set valued mappings is introduced and studied in real reflexive banach spaces following the idea of moudafi we consider a system of generalized equations problems and show its equivalence with the system of generalized mixed implicity equilibrium problems by using a fixed point formulation of the system of generalized equation problems a new iterative algorithm for solving the system of generalized mixed implicity equilibrium problems is suggested and analyzed the strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions these results are new and unify and generalize some recent results in this field

semiparametric model based inference in the presence of missing responses summary we consider a semiparametric model that parameterizes the conditional density ofthe response given covariates but allows the marginal distribution of the covariates to be completely arbitrary responses may be missing a likelihood based imputation estimator and a semi empirical likelihood based estimator for the parameter vector describing the conditional density are defined and proved to be asymptotically normal semi empirical loglikelihood functions for the parameter vector and the response mean are derived it is shown that the two semi empirical loglikelihood functions are distributed asymptotically as weighted x2 and scaled x2 respectively

solutions of the two level problem in terms of biconfluent heun functions five four parametric classes of quantum mechanical two level models permitting solutions in terms of the biconfluent heun function are derived three of these classes are generalizations of the well known classes of landau zener nikitin and crothers it is shown that two other classes describe superand sublinear and essentially nonlinear level crossings as well as processes with three crossing points in particular these classes include two level models where the field amplitude is constant and the detuning varies as 0t 2t 3 or t 1 3 for the essentially nonlinear cubic crossing model t 2t 3 the general solution of the two level problem is shown to be expressed as series of confluent hypergeometric functions

a propensity score adjustment for multiple group structural equation modeling in the behavioral and social sciences quasi experimental and observational studies are used due to the difficulty achieving a random assignment however the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates to estimate average treatment effects when the treatment variable is binary rosenbaum and rubin 1983a proposed adjustment methods for pretreatment variables using the propensity score

sensitivity analysis for nonlinear generalized mixed implicit equilibrium problems with non monotone set valued mappings in this paper we introduce and study a new class of nonlinear generalized mixed implicit equilibrium problems with nonmonotone set valued mappings by using wiener hopf equations and the yosida approximation notion we prove the existence of solutions and analyze the sensitivity of solutions for this class of nonlinear generalized mixed implicit equilibrium problems in hilbert spaces our results are new and extend improve and unify some recent results in this field

an effective bandwidth selector for local least squares regression abstract local least squares kernel regression provides an appealing solution to the nonparametric regression or scatterplot smoothing problem as demonstrated by fan for example the practical implementation of any scatterplot smoother is greatly enhanced by the availability of a reliable rule for automatic selection of the smoothing parameter in this article we apply the ideas of plug in bandwidth selection to develop strategies for choosing the smoothing parameter of local linear squares kernel estimators our results are applicable to odd degree local polynomial fits and can be extended to other settings such as derivative estimation and multiple nonparametric regression an implementation in the important case of local linear fits with univariate predictors is shown to perform well in practice a by product of our work is the development of a class of nonparametric variance estimators based on local least squares ideas and plug in rules for their implementation

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