asymptotically efficient estimation of models defined by convex moment inequalities this paper examines the efficient estimation of partially identified models defined by moment inequalities that are convex in the parameter of interest in such a setting the identified set is itself convex and hence fully characterized by its support function we provide conditions under which despite being an infinite dimensional parameter the support function admits n consistent regular estimators a semiparametric efficiency bound is then derived for its estimation and it is shown that any regular estimator attaining it must also minimize a wide class of asymptotic loss functions in addition we show that the plug in estimator is efficient and devise a consistent bootstrap procedure for estimating its limiting distribution the setting we examine is related to an incomplete linear model studied in beresteanu and molinari 2008 and bontemps magnac and maurin 2012 which further enables us to establish the semiparametric efficiency of their proposed estimators for that problem

bootstrap tests for distributional treatment effects in instrumental variable models this article considers the problem of assessing the distributional consequences of a treatment on some outcome variable of interest when treatment intake is possibly nonrandomized but there is a binaryinstrument available for the researcher such a scenario is common in observational studies and in randomized experiments with imperfect compliance one possible approach to this problem is to compare the counterfactual cumulative distribution functions of the outcome with and without the treatment this article shows how to estimate these distributions using instrumental variable methods and a simple bootstrap procedure is proposed to test distributional hypotheses such as equality of distributions first order and second order stochastic dominance these tests and estimators are applied to the study of the effects of veteran status on the distribution of civilian earnings the results show a negative effect of military service during the vietnam era that appears to be concentrated on the lower tail of

nonparametric tests of stochastic dominance in income distributions tests for stochastic dominance based upon extensions of the goodness of fit test to the nonparametric comparison of income distributions are proposed implemented and compared with indirect tests of second order stochastic dominance currently utilized in income distribution studies

statistical inference for stochastic dominance and for the measurement of poverty and inequality we derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty welfare and inequality this includes estimators of most of the poverty indices currently in use as well as estimators of the curves used to infer stochastic dominance of any order these curves can be used to determine whether poverty inequality or social welfare is greater in one distribution than in another for general classes of indices and for ranges of possible poverty lines we also derive the sampling distribution of the maximal poverty lines up to which we may confidently assert that poverty is greater in one distribution than in another the sampling distribution of convenient dual estimators for the measurement of poverty is also established the statistical results are established for deterministic or stochastic poverty lines as well as for paired or independent samples of incomes our results are briefly illustrated using data for four countries drawn from the luxembourg income study data bases

standard symmetric operators in pontryagin spaces a generalized von neumann formula and minimality of boundary coefficients certain meromorphic matrix valued functions on c r the so called boundary coefficients are characterized in terms of a standard symmetric operator s in a pontryagin space with finite not necessarily equal defect numbers a meromorphic mapping into the defect subspaces of s and a boundary mapping for s under some simple assumptions the boundary coefficients also satisfy a minimality condition it is shown that these assumptions hold if and only if for s a generalized von neumann equality is valid r 2002 elsevier science usa all rights reserved msc primary 47b50 47b25 34b07 47b32 secondary 46c20 47a06

estimation and inference for distribution functions and quantile functions in treatment effect models abstract we propose inverse probability weighted estimators for the distribution functions of the potential outcomes under the unconfoundedness assumption and apply the inverse mapping to obtain the quantile functions we show that these estimators converge weakly to zero mean gaussian processes a simulation method is proposed to approximate these limiting processes based on these results we construct tests for stochastic dominance relations between the potential outcomes monte carlo simulations are conducted to examine the finite sample properties of our tests we apply our test in an empirical example and find that a job training program had a positive effect on incomes

a direct approach to inference in nonparametric and semiparametric quantile models we construct a generic confidence interval for a conditional quantile via the direct approach it avoids estimating the conditional density function of the dependent variable given the covariate and is asymptotically valid for any conditional quantile any conditional quantile estimator and any data structure provided that certain weak convergence of the conditional quantile process holds for the original quantile estimator we also construct a generic confidence band for the conditional quantile function across a range of covariate values by using yang stute estimator and two semiparametric quantile functions we demonstrate the flexibility and simplicity of the direct approach the advantages of our new confidence intervals are borne out in a simulation study

efficient semiparametric estimation of quantile treatment effects this paper develops estimators for quantile treatment effects under the identifying restriction that selection to treatment is based on observable characteristics identification is achieved without requiring computation of the conditional quantiles of the potential outcomes instead the identification results for the marginal quantiles lead to an estimation procedure for the quantile treatment effect parameters that has two steps nonparametric estimation of the propensity score and computation of the difference between the solutions of two separate minimization problems root n consistency asymptotic normality and achievement of the semiparametric efficiency bound are shown for that estimator a consistent estimation procedure for the variance is also presented finally the method developed here is applied to evaluation of a job training program and to a monte carlo exercise results from the empirical application indicate that the method works relatively well even for a data set with limited overlap between treated and controls in the support of covariates the monte carlo study shows that for a relatively small sample size the method produces estimates with good precision and low bias especially for middle quantiles

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

irregular identification support conditions and inverse weight estimation in weighted moment condition models we show a subtle link between identification and estimability that limits the practical usefulness of estimators based on these models in particular if it is necessary for point identification that the weights take arbitrarily large values then the parameter of interest though point identified cannot be estimated at the regular parametric rate and is said to be irregularly identified this rate depends on relative tail conditions and can be as slow in some examples as n 1 4 this nonstandard rate of convergence can lead to numerical instability and or large standard errors we examine two weighted model examples i the binary response model under mean restriction introduced by lewbel 1997 and further generalized to cover endogeneity and selection where the estimator in this class of models is weighted by the density of a special regressor and ii the treatment effect model under exogenous selection rosenbaum and rubin 1983 where the resulting estimator of the average treatment effect is one that is weighted by a variant of the propensity score without strong relative support conditions these models similar to well known identified at infinity models lead to estimators that converge at slower than parametric rate since essentially to ensure point identification one requires some variables to take values on sets with arbitrarily small probabilities or thin sets for the two models above we derive some rates of convergence and propose that one conducts inference using rate adaptive procedures that are analogous to andrews and schafgans 1998 for the sample selection model

the linearization of boundary eigenvalue problems and reproducing kernel hilbert spaces the boundary eigenvalue problems for the adjoint of a symmetric relation s in a hilbert space with finite not necessarily equal defect numbers which are related to the selfadjoint hilbert space extensions of s are characterized in terms of boundary coefficients and the reproducing kernel hilbert spaces they induce 2001 elsevier science inc all rights reserved

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

a study of defuzzification with experts knowledge for deteriorating repairable systems abstract this paper presents ideas on the applications of fuzzy concepts to decision making for deteriorating repairable systems a non homogeneous poisson process nhpp with a power law intensity function is used in this study in general classical bayesian decision methods presume that future states of nature can be characterized as probability events however we do not know what the future will entail probabilistically so we devise a method to consider experts opinions which are usually the absence of sharply defined criteria and to develop a fuzzy bayesian decision process for dealing with such situations two cases of the discrimination problem with deteriorating repairable systems are studied 1 fuzzy states and exact information and 2 fuzzy states and fuzzy information the fuzzy decomposition and arithmetic derivation of the experts opinion are presented to facilitate the development of the bayesian decision process for deteriorating repairable systems

generic inference on quantile and quantile effect functions for discrete outcomes quantile and quantile effect qe functions are important tools for descriptive and causal analysis due to their natural and intuitive interpretation existing inference methods for these functions

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

operators without eigenvalues in finite dimensional vector spaces abstract we introduce the concept of a canonical subspace of c d z and among other results prove the following statements an operator in a finite dimensional vector space has no eigenvalues if and only if it is similar to the operator of multiplication by the independent variable on a canonical subspace of c d z an operator in a finite dimensional pontryagin space is symmetric and has no eigenvalues if and only if it is isomorphic to the operator of multiplication by the independent variable in a canonical subspace of c d z with an inner product determined by a full matrix polynomial nevanlinna kernel

inference based on conditional moment inequalities in this paper we propose an instrumental variable approach to constructing confidence sets cs s for the true parameter in models defined by conditional moment inequalities equalities we show that by properly choosing instrument functions one can transform conditional moment inequalities equalities into unconditional ones without losing identification power based on the unconditional moment inequalities equalities we construct cs s by inverting cramer von mises type or kolmogorov smirnov type tests critical values are obtained using generalized moment selection gms procedures we show that the proposed cs s have correct uniform asymptotic coverage probabilities new methods are required to establish these results because an infinite dimensional nuisance parameter affects the asymptotic distributions we show that the tests considered are consistent against all fixed alternatives and typically have power against n 1 2 local alternatives to some but not all sequences of distributions in the null hypothesis monte carlo simulations for five different models show that the methods perform well in finite samples

quantile and probability curves without crossing this paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions also known as the quantile crossing problem bassett and koenker 1982 the method consists in sorting or monotone rearranging the original estimated non monotone curve into a monotone rearranged curve we show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples establish a functional delta method for rearrangement related operators and derive functional limit theory for the entire rearranged curve and its functionals we also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals our limit results are generic in that they apply to every estimator of a monotone function provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions consequently our results apply to estimation of other econometric functions with monotonicity restrictions such as demand production distribution and structural distribution functions we illustrate the results with an application to estimation of structural distribution and quantile functions using data on vietnam veteran status and earnings

on the reproducing kernel of a pontryagin space of vector valued polynomials abstract we give necessary and sufficient conditions under which the reproducing kernel of a pontryagin space of d 1 vector polynomials is determined by a generalized nevanlinna pair of d d matrix polynomials

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 structure theorem for reproducing kernel pontryagin spaces we illustrate a relationship between reproducing kernel spaces and orthogonal polynomials via a general structure theorem the christofell darboux formula emerges as a limit case

an improved bootstrap test of stochastic dominance we propose a new method of testing stochastic dominance that improves on existing tests based on the standard bootstrap or subsampling the method admits prospects involving infinite as well as finite dimensional unknown parameters so that the variables are allowed to be residuals from nonparametric and semiparametric models the proposed bootstrap tests have asymptotic sizes that are less than or equal to the nominal level uniformly over probabilities in the null hypothesis under regularity conditions this paper also characterizes the set of probabilities so that the asymptotic size is exactly equal to the nominal level uniformly as our simulation results show these characteristics of our tests lead to an improved power property in general the improvement stems from the design of the bootstrap test whose limiting behavior mimics the discontinuity of the original test s limiting distribution

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

efficient propensity score regression estimators of multivalued treatment effects for the treated abstract when a multivalued treatment is randomly assigned conditional on observables valid causal comparisons for a subpopulation treated at a particular treatment level require two propensity scores one for the treated level and one for the counterfactual level we contribute efficient propensity score regression estimators to a class of treatment effects for the treated under the cases when the propensity scores are unknown and when they are known our efficient estimator matches on a normalized propensity score that combines the true propensity score and the nonparametric estimate our asymptotic theory takes into account that the propensity scores are nonparametrically or parametrically estimated as generated regressors

on bezoutians of nonsquare matrix polynomials and inversion of matrices with nonsquare blocks abstract the notion of bezoutian of nonsquare matrix polynomials is defined it is used to establish formulae for the inverse of square matrices partitioned into nonsquare blocks in particular a generalization of the gohberg semencul formula for the inverse of a generalized toeplitz matrix is proved

consistent tests for stochastic dominance methods are proposed for testing stochastic dominance of any pre specified order with primary interest in the distributions of income we consider consistent tests that are similar to kolmogorov smirnov tests of the complete set of restrictions that relate to the various forms of stochastic dominance for such tests in the case of tests for stochastic dominance beyond first order we propose and justify a variety of approaches to inference based on simulation and the bootstrap we compare these approaches to one another and to alternative approaches based on multiple comparisons in the context of a monte carlo experiment and an empirical example