an efficient semiparametric estimator for binary response models this paper proposes an estimator for discrete choice models that makes no assumption concerning the functional form of the choice probability function where this function can be characterized by an index the estimator is shown to be consistent asymptotically normally distributed and to achieve the semiparametric efficiency bound monte carlo evidence indicates that there may be only modest efficiency losses relative to maximum likelihood estimation when the distribution of the disturbances is known and that the small sample behavior of the estimator in other cases is good

automorphisms of the fine grading of sl n c associated with the generalized pauli matrices we consider the grading of sl n c by the group n of generalized pauli matrices the grading decomposes the lie algebra into n2 1 one dimensional subspaces in the article we demonstrate that the normalizer of grading decomposition of sl n c in n is the group sl 2 zn where zn is the cyclic group of order n as an example we consider sl 3 c graded by 3 and all contractions preserving that grading we show that the set of 48 quadratic equations for grading parameters splits into just two orbits of the normalizer of the grading in 3

weyl groups of fine gradings on matrix algebras octonions and the albert algebra given a grading a g gag on a nonassociative algebra a by an abelian group g we have two subgroups of aut a the automorphisms that stabilize each component ag as a subspace and the automorphisms that permute the components by the weyl group of we mean the quotient of the latter subgroup by the former in the case of a cartan decomposition of a semisimple complex lie algebra this is the automorphism group of the root system i e the so called extended weyl group a grading is called fine if it cannot be refined we compute the weyl groups of all fine gradings on matrix algebras octonions and the albert algebra over an algebraically closed field of characteristic different from 2 in the case of the albert algebra

nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates abstract allowing for the existence of irrelevant covariates we study the problem of estimating a conditional quantile function nonparametrically with mixed discrete and continuous data we estimate the conditional quantile regression function using the check function based kernel method and suggest a data driven cross validation cv approach to simultaneously determine the optimal smoothing parameters and remove the irrelevant covariates when the number of covariates is large we first use a screening method to remove the irrelevant covariates and then apply the cv criterion to those that survive the screening procedure simulations and an empirical application demonstrate the usefulness of the proposed methods

on lie gradings ii abstract to obtain fine gradings of gl n c it is necessary to study maximal abelian subgroups mad subgroups of diagonizable automorphisms in a ut gl n c we described two finite sets h n and k n such that each mad subgroup consisting only from inner automorphisms is conjugated to some element of h n and each mad subgroup containing at least one outer automorphism is conjugated to some element of k n using these results concerning k n we then easily find all mad subgroups in a ut o n c for n 8 and in a ut sp 2n c

on the efficiency and optimality of allocations ii nikolaos in this work we study the problem of characterizing efficient price efficient and optimal allocations in a very general economic model with a continuum of agents and an infinite dimensional commodity space we do that using the theory of concave normal integrands and clarke s theory of generalized gradients as well as certain results from geometric functional analysis we also consider approximations of those notions and study their properties using the theory of varepsilon subdiflerentiation and ekeland s variational principal then we examine those concepts in the context of a particular sector of the enonomy using single valued and multivalued conditional expectations and martingale theory finally we study stability questions using the kuratowski mosco convergence of sets and the epi convergence tau convergence of closed functions

group gradings on associative algebras abstract let r g g rg be a g graded ring we describe all types of gradings on r if g is torsion free and r is artinian semisimple if r is a matrix algebra over an algebraically closed field f then we give a description of all g gradings on r provided that g is an abelian group in the case of an abelian group g we also classify all finite dimensional graded simple algebras and finite dimensional graded division algebras over an algebraically closed field of characteristic zero

convex integral functionals we study nonlinear integral functionals determined by normal convex integrands first we obtain expressions for their convex conjugate their e subdifferential e 0 and their directional derivative then we derive a necessary and sufficient condition for the existence of an approximate solution for the continuous infimal convolution we also obtain general conditions which guarantee the interchangeability of the conditional expectation and subdifferential operators finally we examine the conditional expectation of random sets

shrinkage for categorical regressors abstract this paper introduces a flexible regularization approach that reduces point estimation risk of group means stemming from e g categorical regressors quasi experimental data or panel data models the loss function is penalized by adding weighted squared l 2 norm differences between group location parameters and informative first stage estimates under quadratic loss the penalized estimation problem has a simple interpretable closed form solution that nests methods established in the literature on ridge regression discretized support smoothing kernels and model averaging methods we derive risk optimal penalty parameters and propose a plug in approach for estimation the large sample properties are analyzed in an asymptotic local to zero framework by introducing a class of sequences for close and distant systems of locations that is sufficient for describing a large range of data generating processes we provide the asymptotic distributions of the shrinkage estimators under different penalization schemes the proposed plug in estimator uniformly dominates the ordinary least squares estimator in terms of asymptotic risk if the number of groups is larger than three monte carlo simulations reveal robust improvements over standard methods in finite samples real data examples of estimating time trends in a panel and a difference in differences study illustrate potential applications

pairwise local fisher and naive bayes improving two standard discriminants abstract the fisher discriminant is probably the best known likelihood discriminant for continuous data another benchmark discriminant is the naive bayes which is based on marginals only in this paper we extend both discriminants by modeling dependence between pairs of variables in the continuous case this is done by local gaussian versions of the fisher discriminant in the discrete case the naive bayes is extended by taking geometric averages of pairwise joint probabilities we also indicate how the two approaches can be combined for mixed continuous and discrete data the new discriminants show promising results in a number of simulation experiments and real data illustrations

uniformly semiparametric efficient estimation of treatment effects with a continuous treatment this article studies identification estimation and inference of general unconditional treatment effects models with continuous treatment under the ignorability assumption we show identification of the parameters of interest the dose response functions under the assumption that selection to treatment is based on observables we propose a semiparametric two step estimator and consider estimation of the dose response functions through moment restriction models with generalized residual functions that are possibly nonsmooth this general formulation includes average and quantile treatment effects as special cases the asymptotic properties of the estimator are derived namely uniform consistency weak convergence and semiparametric efficiency we also develop statistical inference procedures and establish the validity of a bootstrap approach to implement these methods in practice monte carlo simulations show that the proposed methods have good finite sample properties finally we apply the proposed

using least squares and tobit in second stage dea efficiency analyses the paper examines second stage dea efficiency analyses within the context of a censoring data generating process dgp and a fractional data dgp when efficiency scores are treated as descriptive measures of the relative performance of units in the sample it is argued that the efficiency scores are not generated by a censoring process but are fractional data tobit estimation in this situation is inappropriate in contrast ordinary least squares is a consistent estimator and if white s white h 1980 a heteroskedastic consistent covariance matrix and a direct test for heteroskedasticity econometrica 48 817 838 heteroskedastic consistent standard errors are calculated large sample tests can be performed which are robust to heteroskedasticity and the distribution of the disturbances for a more refined analysis papke and wooldridge s papke l e wooldridge j m 1996 econometric methods for fractional response variables with an application to 401 k plan participation rates journal of applied econometrics 11 6 619 632 method has some advantages but is more complex and requires special programming

fine gradings on simple classical lie algebras abstract the fine abelian group gradings on the simple classical lie algebras including d 4 over algebraically closed fields of characteristic 0 are determined up to equivalence this is achieved by assigning certain invariant to such gradings that involve central graded division algebras and suitable sesquilinear forms on free modules over them

nonparametric censored and truncated regression we propose new estimators of the latent regression function in nonparametric cen sored and truncated regression models our estimators are computationally convenient consisting only of two nonparametric regressions and a univariate integral we establish consistency and asymptotic normality for an implementation based on local linear ker nel estimators an extension permits estimation in the presence of a general form of heteroscedasticity both the function m and the distribution f of the error e are unknown the errors are not assumed to be symmetric this paper provides a simple consistent estimator of m x k for some constant k under an additional tail condition we provide a consistent estimator of m x when m is the conditional mean function of the uncensored population also we show that f can be estimated given m x the proposed estimator is extended to deal with the truncated regression model where yi is only observed when it is not censored we also describe extensions to deal with a general form of heteroskedasticity in which the distribution of e could depend in unknown ways on a subset of elements of x for any continuously distributed element xk of x let mk x am x axk we also provide direct estimators of the derivatives mk x in both the censored and truncated regression models these derivatives are interpretable as the marginal effect of a change in x on the underlying uncensored population they can also be used to test or estimate parametric or semiparametric specifications of m x for example mk x is constant if m x is linear in xk and mk x depends only on xk if m x is additive in a function of xk

local likelihood estimation of truncated regression and its partial derivatives theory and application in this paper we propose a very flexible estimator in the context of truncated regression that does not require parametric assumptions to do this we adapt the theory of local maximum likelihood estimation we provide the asymptotic results and illustrate the performance of our estimator on simulated and real data sets our estimator performs as good as the fully parametric estimator when the assumptions for the latter hold but as expected much better when they do not provided that the curse of dimensionality problem is not the issue overall our estimator exhibits a fair degree of robustness to various deviations from linearity in the regression equation and also to deviations from the specification of the error term so the approach shall prove to be very useful in practical applications where the parametric form of the regression or of the distribution is rarely known

gradings and symmetries on heisenberg type algebras abstract we describe the fine group gradings on the heisenberg algebras on the heisenberg superalgebras and on the twisted heisenberg algebras we compute the weyl groups of these gradings also the results obtained respect to heisenberg superalgebras are applied to the study of heisenberg lie color algebras

law of large numbers for random sets and allocation processes in this paper we establish a strong law of large numbers for unbounded random sets and then apply it to an optimization problem arising in allocation processes under uncertainty

fine grading of sl p2 c generated by tensor product of generalized pauli matrices and its symmetries study of the normalizer of the mad group corresponding to a fine grading offers the most important tool for describing symmetries in the system of nonlinear equations connected with contraction of a lie algebra one fine grading that is always present in any lie algebra sl n c is the pauli grading the mad group corresponding to it is generated by generalized pauli matrices for such mad group we already know its normalizer its quotient group is isomorphic to the lie group sl 2 zn z2 in this paper we deal with a more complicated situation namely that the fine grading of sl p2 c is given by a tensor product of the pauli matrices of the same order p p being a prime we describe the normalizer of the corresponding mad group and we show that its quotient group is isomorphic to sp 4 fp z2 where fp is the finite field with p elements

projection pursuit density estimation abstract the projection pursuit methodology is applied to the multivariate density estimation problem the resulting nonparametric procedure is often less biased than the kernel and near neighbor methods in addition graphical information is produced that can be used to help gain geometric insight into the multivariate data distribution

an alternative method of cross validation for the smoothing of density estimates cross validation with kullback leibler loss function has been applied to the choice of a smoothing parameter in the kernel method of density estimation a framework for this problem is constructed and used to derive an alternative method of cross validation based on integrated squared error recently also proposed by rudemo 1982 hall 1983 has established the consistency and asymptotic optimality of the new method for small and moderate sized samples the performances of the two methods of cross validation are compared on simulated data and specific examples

estimation and inference in two stage semi parametric models of production processes many papers have regressed non parametric estimates of productive efficiency on environmental variables in two stage procedures to account for exogenous factors that might affect firms performance none of these have described a coherent data generating process dgp moreover conventional approaches to inference employed in these papers are invalid due to complicated unknown serial correlation among the estimated efficiencies we first describe a sensible dgp for such models we propose single and double bootstrap procedures both permit valid inference and the double bootstrap procedure improves statistical efficiency in the second stage regression we examine the statistical performance of our estimators using monte carlo experiments

nonparametric tests of the markov hypothesis in continuous time models we propose several statistics to test the markov hypothesis for mixing stationary processes sampled at discrete time intervals our tests are based on the chapman kolmogorov equation we establish the asymptotic null distributions of the proposed test statistics showing that wilks s phenomenon holds we compute the power of the test and provide simulations to investigate the finite sample performance of the test statistics when the null model is a diffusion process with alternatives consisting of models with a stochastic mean reversion level stochastic volatility and jumps

a family of nonparametric density estimation algorithms a new methodology for density estimation is proposed the methodology which builds on the one developed by tabak and vanden eijnden normalizes the data points through the composition of simple maps the parameters of each map are determined through the maximization of a local quadratic approximation to the log likelihood various candidates for the elementary maps of each step are proposed criteria for choosing one includes robustness computational simplicity and good behavior in high dimensional settings a good choice is that of localized radial expansions which depend on a single parameter all the complexity of arbitrary possibly convoluted probability densities can be built through the composition of such simple maps 2012 wiley periodicals inc

fine gradings on simple exceptional jordan pairs and triple systems abstract we give a classification up to equivalence of the fine group gradings by abelian groups on the jordan pairs and triple systems of types bi cayley and albert under the assumption that the base field is algebraically closed of characteristic different from 2 the associated weyl groups are computed we also determine for each fine grading on the bi cayley and albert pairs the induced grading on the exceptional simple lie algebra given by the tits kantor koecher construction

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

the performance of estimators based on the propensity score we investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required like inverse probability weighting kernel and other variants of matching as well as different parametric models the simulation design used is based on real data usually employed for the evaluation of labour market programmes in germany we vary several dimensions of the design that are of practical importance like sample size the type of the outcome variable and aspects of the selection process we find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators a conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property

classification of group gradings on simple lie algebras of types a b c and d abstract for a given abelian group g we classify the isomorphism classes of g gradings on the simple lie algebras of types a n n 1 b n n 2 c n n 3 and d n n 4 in terms of numerical and group theoretical invariants the ground field is assumed to be algebraically closed of characteristic different from 2

convergence and representation theorems for set valued random processes abstract in this paper we study set valued random processes in discrete time and with values in a separable banach space we start with set valued martingales and prove various convergence and regularity results then we turn our attention to larger classes of set valued processes so we introduce and study set valued amarts and set valued martingales in the limit finally we prove a useful property of the set valued conditional expectation

unobserved heterogeneity and endogeneity in nonparametric frontier estimation in production theory and eciency analysis rm eciencies are measured by their distances to a production frontier which is the geometrical locus of optimal combinations of inputs and outputs it is today recognized that in the presence of heterogenous conditions like environmental factors that influence the shape and the position of the frontier traditional measures of efficiency obtained in the space of inputs outputs have no sensible economic meaning this is because the benchmark frontier may not be attainable for a firm facing different heterogenous conditions using a nonparametric approach this can be corrected by using conditional frontiers and conditional efficiency scores developed in the literature in this paper we extend these concepts in the case where the heterogeneity is not observed we propose and analyze a model where the heterogeneity variable is linked to a particular input or output it is defined as the part of the input or the output independent from some instrumental variable through a nonseparable nonparametric model we discuss endogeneity issues involved in this model under certain regularity assumptions we show that the model is identified we propose nonparametric estimators of the conditional frontier and the conditional efficiency score and analyze their asymptotic properties when using fdh estimators we prove the asymptotic convergence to a weibull distribution whereas when using the robust order m estimators we obtain the asymptotic normality of the estimators the method is illustrated with some simulated and real data examples a monte carlo experiment shows how the procedure works for finite samples

gradings on symmetric composition algebras abstract the group gradings on the symmetric composition algebras over arbitrary fields are classified applications of this result to gradings on the exceptional simple lie algebras are considered too

dimension reduction and adaptation in conditional density estimation an orthogonal series estimator of the conditional density of a response given a vector of continuous and ordinal nominal categorical predictors is suggested the estimator is based on writing a conditional density as a sum of orthogonal projections on all possible subspaces of reduced dimensionality and then estimating each projection via a shrinkage procedure the shrinkage procedure uses a universal thresholding and a dyadic blockwise shrinkage for low and high frequencies respectively the estimator is data driven is adaptive to underlying smoothness of a conditional density and attains a minimax rate of the mean integrated squared error convergence furthermore if a conditional density depends only on a subgroup of predictors then the estimator seizes the opportunity and attains a corresponding minimax rate of convergence the latter property relaxes the notorious curse of dimensionality moreover the estimator is fast because neither projections nor shrinkages are computation intensive a nu

a crossvalidation method for estimating conditional densities summary we extend the idea of crossvalidation to choose the smoothing parameters of the double kernel local linear regression for estimating a conditional density our selection rule optimises the estimated conditional density function by minimising the integrated squared error we also discuss three other bandwidth selection rules an ad hoc method used by fan et al 1996 a bootstrap method of hall et al 1999 for bandwidth selection in the estimation of conditional distribution functions modified by bashtannyk hyndman 2001 to cover conditional density functions and finally a simple approach proposed by hyndman yao 2002 the performance of the new approach is compared with these three methods by simulation studies and our method performs outstandingly well the method is illustrated by an application to estimating the transition density and the value at risk of treasury bill data

growth and convergence a profile of distribution dynamics and mobility in this paper we focus primarily on the dynamic evolution of the world distribution of growth rates in per capita gdp we propose new concepts and measures of convergence or divergence that are based on entropy distances and dominance relations between groups of countries over time we update the sample period to include the most recent decade of data available and we offer traditional parametric and new nonparametric estimates of the most widely used growth regressions for two important subgroups of countries oecd and non oecd traditional parametric models are rejected by the data however using robust nonparametric methods we find strong evidence in favor of polarization and within group mobility

nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters we consider nonparametric semiparametric estimation and testing of econometric models with data dependent smoothing parameters most of the existing works on asymptotic distributions of a nonparametric semiparametric estimator or a test statistic are based on some deterministic smoothing parameters while in practice it is important to use data driven methods to select the smoothing parameters in this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters we also allow for general weakly dependent data

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

nonparametric transition based tests for jump diffusions we develop a specification test for the transition density of a discretely sampled continuous time jump diffusion process based on a comparison of a nonparametric estimate of the transition density or distribution function with their corresponding parametric counterparts assumed by the null hypothesis as a special case our method applies to pure diffusions we provide a direct comparison of the two densities for an arbitrary specification of the null parametric model using three different discrepancy measures between the null and alternative transition density and distribution functions we establish the asymptotic null distributions of proposed test statistics and compute their power functions we investigate the finite sample properties through simulations and compare them with those of other tests this article has supplementary material online

extent to which least squares cross validation minimises integrated square error in nonparametric density estimation let ho o and c be the windows which minimise mean integrated square error integrated square error and the least squares cross validatory criterion respectively for kernel density estimates it is argued that o not ho should be the benchmark for comparing different data driven approaches to the determination of window size asymptotic properties of ho o and c o and of differences between integrated square errors evaluated at these windows are derived it is shown that in comparison to the benchmark o the observable window c performs as well as the so called optimal but unattainable window ho to both first and second order

nonparametric frontier estimation a robust approach most nonparametric methods for estimating production frontiers data envelopment analysis and free disposal hall fdh are based on envelopment techniques statistical inference based on these estimators is available but by construction they are very sensitive to extreme values or outliers we propose a nonparametric estimator which is more robust to these extreme values it is based on a concept of expected minimum input function or expected maximal output function we show how this function is related to the efficient frontier itself the resulting estimator is related to the fdh estimator but it will not envelop all the data the asymptotic theory is provided our approach includes the multiple input and multiple output cases c 2002 elsevier science s a all rights reserved

conditional density estimation in a regression setting regression problems are traditionally analyzed via univariate characteristics like the regression function scale function and marginal density of regression errors these characteristics are useful and informative whenever the association between the predictor and the response is relatively simple more detailed information about the association can be provided by the conditional density of the response given the predictor for the first time in the literature this article develops the theory of minimax estimation of the conditional density for regression settings with fixed and random designs of predictors bounded and unbounded responses and a vast set of anisotropic classes of conditional densities the study of fixed design regression is of special interest and novelty because the known literature is devoted to the case of random predictors for the aforementioned models the paper suggests a universal adaptive estimator which i matches performance of an oracle that knows both an underlying model and an estimated conditional density ii is sharp minimax over a vast class of anisotropic conditional densities iii is at least rate minimax when the response is independent of the predictor and thus a bivariate conditional density becomes a univariate density iv is adaptive to an underlying design fixed or random of predictors

bayesian modeling of joint and conditional distributions in this paper we study a bayesian approach to exible modeling of conditional distributions the approach uses a exible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution we use a nite mixture of multivariate normals fmmn to estimate the joint distribution the conditional distributions can then be assessed analytically or through simulations the discrete variables are handled through the use of latent variables the estimation procedure employs an mcmc algorithm we provide a characterization of the kullback leibler closure of fmmn and show that the joint and conditional predictive densities implied by fmmn model are consistent estimators for a large class of data generating processes with continuous and discrete observables the method can be used as a robust regression model with discrete and continuous dependent and independent variables and as a bayesian alternative to semi and non parametric models such as quantile and kernel regression in experiments the method compares favorably with classical nonparametric and alternative bayesian methods

random fuzzy sets and fuzzy martingales abstract the present paper is motivated by the definitions and properties developed by puri and ralescu 1986 we study the random fuzzy sets and their relationship to fuzzy set valued measures in a separable banach space using the conditional expectations of random fuzzy sets we introduce the concept of fuzzy martingales some properties and convergence theorems of fuzzy martingales are investigated

gradings on octonions abstract all the different ways of grading any cayley dickson or octonion algebra as well as the associated central simple malcev algebras will be obtained

on the conditional expectation and convergence properties of random sets in this paper we study random sets with values in a separable banach space first we establish several useful properties of the set valued conditional expectation and then prove some convergence theorems for set valued amarts and uniform amarts using the weak kuratowski mosco and hausdorff modes of set convergence

environmental factors in frontier estimation a monte carlo analysis we compare three recently developed frontier estimators namely the conditional dea daraio and simar 2005 2007b the latent class sfa greene 2005 orea and kumbhakar 2004 and the stonezd approach johnson and kuosmanen 2011 by means of monte carlo simulation we focus on their ability to identify production frontiers and efficiency rankings in the presence of environmental factors our simulations match features of real life datasets and cover a wide range of scenarios with variations in sample size distribution of noise and inefficiency as well as in distributions intensity and number of environmental variables our results provide insight in the finite sample properties of the estimators while also identifying estimator specific characteristics overall the latent class approach is found to perform best although in many cases stonezd shows a similar performance performance of cdea is most often inferior

a class of smooth estimators for discrete distributions summary this paper presents a class of smooth weight function estimators for discrete distributions any estimator in the class depends on choosing a parameterized set of weights the resulting estimators are strongly consistent and asymptotically normal under mild regularity conditions a general procedure for choosing the weight function smoothing parameter is given along with specific solutions in some cases mean squared error comparisons with the maximum likelihood estimator based on large sample theory and small sample simulations are obtained typically the weight function estimates yield significantly smaller mean squared error in these comparisons

weyl groups of some fine gradings on e6 abstract the weyl groups of the fine gradings on the exceptional lie algebra e 6 whose universal grading group is infinite are computed

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

optimal bandwidth selection for conditional efficiency measures a data driven approach in productivity analysis an important issue is to detect how external environmental factors exogenous to the production process and not under the control of the producer might in uence the production process and the resulting efficiency of the rms most of the traditional approaches proposed in the literature have serious drawbacks an alternative approach is to describe the production process as being conditioned by a given value of the environmental variables cazals florens and simar 2002 daraio and simar 2005 this de nes conditional efficiency measures where the production set in the input output space may depend on the value of the external variables the statistical properties of nonparametric estimators of these conditional measures are now established jeong park and simar 2008 these involve the estimation of a nonstandard conditional distribution function which requires the speci cation of a smoothing parameter a bandwidth so far only the asymptotic optimal order of this bandwidth has been established this is of little interest for the practitioner in this paper we ll this gap and we propose a data driven technique for selecting this parameter in practice the approach based on a least squares cross validation procedure lscv provides an optimal bandwidth that minimizes an appropriate weighted integrated squared error ise the method is carefully described and exempli ed with some simulated data with univariate and multivariate environmental factors an application on real data performances of mutual funds illustrates how this new optimal method of bandwidth selection works in practice

probabilistic characterization of directional distances and their robust versions in productivity analysis the performance of production units is measured through the distance of the individual decision making units dmu to the technology which is defined as the frontier of the production set most of the existing methods farrell debreu and shephard radial measures input or output oriented and hyperbolic distance functions rely on multiplicative measures of the distance and so require to deal with strictly positive inputs and outputs this can be critical when the data contain zero or negative values as in financial data bases for the measure of funds performances directional distance function is an alternative that can be viewed as an additive measure of e ciency we show in this paper that using a probabilistic formulation of the production process the directional distance can be expressed as simple radial or hyperbolic distance up to a simple transformation of the inputs outputs space this allows to propose simple methods of estimation but also to transfer easily most of the known properties of the estimators shared by the radial and hyperbolic distances in addition the formulation allows to define robust directional distances in the lines of quantileor order m partial frontiers finally we can also define conditional directional distance functions conditional to environmental factors to illustrate the methodology we show how it can be implemented using a mutual funds database

the symmetries of the fine gradings of sl nk c associated with direct product of pauli groups a grading of a lie algebra is called fine if it could not be further refined for a fine grading of a simple lie algebra we define its weyl group to describe the symmetry of this grading it is already known that the weyl group of the fine grading of sl n c induced by the action of the group n of the generalized pauli matrices of rank n is sl 2 zn where zn is the cyclic group of order n in this paper we consider the fine grading of sl nk c induced by the action of the group of k fold tensor product of the generalized pauli matrices of rank n we prove that its weyl group is sp 2k zn and is generated by transvections therefore this generalizes the previous result

doob s stopping theorem for fuzzy super sub martingales with discrete time fuzzy random variables are introduced as random variables whose values are not reals but fuzzy sets the concepts of fuzzy conditional expectation and fuzzy super sub martingales are given in this paper we study doob s stopping theorem on fuzzy super sub martingales with discrete parameters

essential convex closure of a family of random sets and its applications abstract in this paper the essential convex closure of a family of random sets is defined and its properties are studied by the essential convex closure a more general optional sampling theorem for set valued super sub martingales is proved and the k m convergence of the unbounded set valued superpramarts is studied

a kernel based parametric method for conditional density estimation a conditional density function which describes the relationship between response and explanatory variables plays an important role in many analysis problems in this paper we propose a new kernel based parametric method to estimate conditional density an exponential function is employed to approximate the unknown density and its parameters are computed from the given explanatory variable via a nonlinear mapping using kernel principal component analysis kpca we develop a new kernel function which is a variant to polynomial kernels to be used in kpca the proposed method is compared with the nadaraya watson estimator through numerical simulation and practical data experimental results show that the proposed method outperforms the nadaraya watson estimator in terms of revised mean integrated squared error rmise therefore the proposed method is an effective method for estimating the conditional densities

a consistent model specification test with mixed discrete and continuous data in this paper we propose a nonparametric kernel based model specification test that can be used when the regression model contains both discrete and continuous regressors we employ discrete variable kernel functions and we smooth both the discrete and continuous regressors using least squares cross validation cv methods the test statistic is shown to have an asymptotic normal null distribution we also prove the validity of using the wild bootstrap method to approximate the null distribution of the test statistic the bootstrap being our preferred method for obtaining the null distribution in practice simulations show that the proposed test has significant power advantages over conventional kernel tests which rely upon frequency based nonparametric estimators that require sample splitting to handle the presence of discrete regressors

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

nonparametric estimation of a generalized additive model with an unknown link function mean of a random scalar y conditional on a random vector x e rd let h x e yix x denote the conditional mean function this paper is concerned with estimating h under weak assumptions about its functional form when x is a multidimensional continuous random variable the paper describes a model that nests single index additive and multiplicative models and that can be estimated with a faster rate of convergence in probability than can a fully nonparametric model nonparametric estimation of h is usually unattractive when x is multidimensional the rate of convergence of nonparametric estimators decreases rapidly as the dimension of x increases and nonparametric estimates can be very imprecise with samples of practical size when x is multidimensional the curse of dimensionality this problem can be overcome through the use of dimension reduction methods they reduce the effective dimension of the estimation problem by making assumptions about the functional form of h that are stronger than those of a fully nonparametric estimator but weaker than those of a finite dimensional parametric model one method of dimension reduction is semiparametric single index modeling the best known and most easily estimated semiparametric single index model assumes that 1 1 h x g 3 x where 3 is an unknown d x 1 vector and g is an unknown function the vector 3 can be estimated with an n 1 2 rate of convergence in probability which is the rate that would be obtained if g were known han 1987 hardle and stoker 1989 horowitz and hardle 1996 ichimura 1993 klein and spady 1993 newey and stoker 1993 powell stock and stoker 1989 sherman 1993 stoker 1991 g can be estimated with the rate of convergence n r 2r 1 where r is an integer that depends on the smoothness of g but not on d dimension reduction can also be achieved by using a nonparametric generalized additive model in such a model