nonparametric instrumental variables estimation for efficiency frontier the paper investigates endogeneity issues in nonparametric frontier models it considers a nonseparable model for a cost function c y u where c and y are the cost and the output u is uniform in 0 1 and is increasing with respect to u the cost frontier corresponds to u 0 and u can be interpreted as a normalized level of inefficiency the endogeneity issue arises when y is dependent of u for identification and estimation we use a nonparametric instrumental variables estimator of the model for fixed value u and obtain an estimate of the quantile cost frontier y this involves the solution of a non linear integral equation if the true frontier y 0 is wanted it is then estimated by estimating the bias correction y 0 y under additional regularity conditions the procedure is illustrated through a simulated sample and with an empirical application to the efficiency of post offices

kernel weighted gmm estimators for linear time series models abstract this paper analyzes the higher order asymptotic properties of generalized method of moments gmm estimators for linear time series models using many lags as instruments a data dependent moment selection method based on minimizing the approximate mean squared error is developed in addition a new version of the gmm estimator based on kernel weighted moment conditions is proposed it is shown that kernel weighted gmm estimators can reduce the asymptotic bias compared to standard gmm estimators kernel weighting also helps to simplify the problem of selecting the optimal number of instruments a feasible procedure similar to optimal bandwidth selection is proposed for the kernel weighted gmm estimator

asymptotic optimality of cl and generalized cross validation in ridge regression with application to spline smoothing the asymptotic optimality of mallows c l and generalized cross validation is demonstrated in the setting of ridge regression an application is made to spline smoothing in nonparametric regression a counterexample is given to help understand why sometimes gcv may not be asymptotically optimal the coefficient of variation for the eigenvalues of the information matrix must be large in order to guarantee the optimality of gcv the proff is based on the connection between gcv and stein s unbiased risk estimate

estimation of nonparametric models with simultaneity we introduce methods for estimating nonparametric nonadditive models with simultaneity the methods are developed by directly connecting the elements of the structural system to be estimated with features of the density of the observable variables such as ratios of derivatives or averages of products of derivatives of this density the estimators are therefore easily computed functionals of a nonparametric estimator of the density of the observable variables we consider in detail a model where to each structural equation there corresponds an exclusive regressor and a model with one equation of interest and one instrument that is included in a second equation for both models we provide new characterizations of observational equivalence on a set in terms of the density of the observable variables and derivatives of the structural functions based on those characterizations we develop two estimation methods in the first method the estimators of the structural derivatives are calculated by a simple matrix inversion and matrix multiplication analogous to a standard least squares estimator but with the elements of the matrices being averages of products of derivatives of nonparametric density estimators in the second method the estimators of the structural derivatives are calculated in two steps in a first step values of the instrument are found at which the density of the observable variables satisfies some properties in the second step the estimators are calculated directly from the values of derivatives of the density of the observable variables evaluated at the found values of the instrument we show that both pointwise estimators are consistent and asymptotically normal

identification and estimation of triangular simultaneous equations models without additivity this paper uses control variables to identify and estimate models with nonseparable multidimensional disturbances triangular simultaneous equations models are considered with instruments and disturbances that are independent and a reduced form that is strictly monotonic in a scalar disturbance here it is shown that the conditional cumulative distribution function of the endogenous variable given the instruments is a control variable also for any control variable identification results are given for quantile average and policy effects bounds are given when a common support assumption is not satisfied estimators of identified objects and bounds are provided and a demand analysis empirical example is given

instrumental variable estimation of nonseparable models there are many environments where knowledge of a structural relationship is required to answer questions of interest also nonseparability of a structural disturbance is a key feature of many models here we consider nonparametric identification and estimation of a model that is monotonic in a nonseparable scalar disturbance which disturbance is independent of instruments this model leads to conditional quantile restrictions we give local identification conditions for the structural equations from those quantile restrictions we find that a modified completeness condition is sufficient for local identification we also consider estimation via a nonparametric minimum distance estimator the estimator minimizes the sum of squares of predicted values from a nonparametric regression of the quantile residual on the instruments we show consistency of this estimator

rates of clustering for some gaussian self similar processes the analogue of strassen s functional law of the iterated logarithm in known for many gaussian processes which have suitable scaling properties and here we establish rates at which this convergence takes place we provide a new proof of the best upper bound for the convergence tok by suitably normalized brownian motion and then continue with this method to get similar bounds for the brownian sheet and other self similar gaussian processes the previous method which produced these results for brownian motion in 1 was highly dependent on many special properties unavailable when dealing with other gaussian processes

testing a parametric quantile regression model with an endogenous explanatory variable against a nonparametric alternative abstract this paper is concerned with inference about a function g that is identified by a conditional quantile restriction involving instrumental variables the paper presents a test of the hypothesis that g belongs to a finite dimensional parametric family against a nonparametric alternative the test is not subject to the ill posed inverse problem of nonparametric instrumental variable estimation under mild conditions the test is consistent against any alternative model in large samples its power is arbitrarily close to 1 uniformly over a class of alternatives whose distance from the null hypothesis is proportional to n 1 2 where n is the sample size monte carlo simulations illustrate the finite sample performance of the test

efficient estimation in models with independence restrictions abstract unconditional and conditional independence restrictions are used in many econometric models to identify their parameters however there are few results about efficient estimation procedures for finite dimensional parameters under these independence restrictions this paper computes the efficiency bound for finite dimensional parameters under independence restrictions and proposes an estimator that is consistent asymptotically normal and which achieves the efficiency bound the estimator is based on a growing number of zero covariance conditions that are asymptotically equivalent to the independence restriction the results are illustrated with examples including an instrumental variables regression model and partially linear regression models a small monte carlo study is performed to investigate the estimator s small sample properties and to quantify the efficiency gains that can be made by using the proposed efficient estimator

bounding quantile demand functions using revealed preference inequalities this paper develops a new technique for the estimation of consumer demand models with unobserved heterogeneity subject to revealed preference inequality restrictions particular attention is given to nonseparable heterogeneity the inequality restrictions are used to identify bounds on quantile demand functions a nonparametric estimator for these bounds is developed and asymptotic properties are derived an empirical application using data from the u k family expenditure survey illustrates the usefulness of the methods by deriving bounds and con dence sets for estimated quantile demand functions

efficient estimation of general dynamic models with a continuum of moment conditions there are two difficulties with the implementation of the characteristic function based estimators first the optimal instrument yielding the ml efficiency depends on the unknown probability density function second the need to use a large set of moment conditions leads to the singularity of the covariance matrix we resolve the two problems in the framework of gmm with a continuum of moment conditions a new optimal instrument relies on the double indexing and as a result has a simple exponential form the singularity problem is addressed via a penalization term we introduce hac type estimators for non markov models a simulated method of moments is proposed for non analytical cases

analysis and geometry on manifolds with integral ricci curvature bounds ii we extend several geometrical results for manifolds with lower ricci curvature bounds to situations where one has integral lower bounds in particular we generalize colding s volume convergence results and extend the cheeger colding splitting theorem

finite sample inference for quantile regression models abstract under minimal assumptions finite sample confidence bands for quantile regression models can be constructed these confidence bands are based on the conditional pivotal property of estimating equations that quantile regression methods solve and provide valid finite sample inference for linear and nonlinear quantile models with endogenous or exogenous covariates the confidence regions can be computed using markov chain monte carlo mcmc methods we illustrate the finite sample procedure through two empirical examples estimating a heterogeneous demand elasticity and estimating heterogeneous returns to schooling we find pronounced differences between asymptotic and finite sample confidence regions in cases where the usual asymptotics are suspect

absorption semigroups their generators and schrodinger semigroups on presente des resultats de perturbations pour des c 0 semi groupes on considere le probleme aux valeurs initiales pour l equation de la chaleur avec absorption avec une solution dans l p r v avec une mauvaise fonction v r r on considere le meme probleme dans l 2 r pour l equation de schrodinger

applied nonparametric instrumental variables estimation instrumental variables are widely used in applied econometrics to achieve identification and carry out estimation and inference in models that contain endogenous explanatory variables in most applications the function of interest e g an engel curve or demand function is assumed to be known up to finitely many parameters e g a linear model and instrumental variables are used identify and estimate these parameters however linear and other finite dimensional parametric models make strong assumptions about the population being modeled that are rarely if ever justified by economic theory or other a priori reasoning and can lead to seriously erroneous conclusions if they are incorrect this paper explores what can be learned when the function of interest is identified through an instrumental variable but is not assumed to be known up to finitely many parameters the paper explains the differences between parametric and nonparametric estimators that are important for applied research describes an easily implemented nonparametric instrumental variables estimator and presents empirical examples in which nonparametric methods lead to substantive conclusions that are quite different from those obtained using standard parametric estimators

a closed form estimator for quantile treatment effects with endogeneity abstract this paper studies the estimation of quantile treatment effects based on the instrumental variable quantile regression ivqr model chernozhukov and hansen 2005 i develop a class of flexible plug in estimators based on closed form solutions derived from the ivqr moment conditions the proposed estimators remain tractable and root n consistent while allowing for rich patterns of effect heterogeneity functional central limit theorems and bootstrap validity results for the estimators of the quantile treatment effects and other functionals are provided monte carlo simulations demonstrate favorable finite sample properties of the proposed approach i apply my method to reanalyze the causal effect of 401 k plans

on the almost sure behavior of sums of iid random variables in hilbert space we study the almost sure behavior of sums of operatorname iid random variables satisfying the bounded lil in hilbert space we show that the almost sure behavior is different from the gaussian case whenever the second strong moments are infinite a law of the k times iterated logarithm is established which refines the bounded lil the interesting feature here is that contrary to the known conditions for the bounded lil one needs not only moment type conditions but also a nice structure of the covariance operator

estimation of nonparametric conditional moment models with possibly nonsmooth moments this paper studies nonparametric estimation of conditional moment models in which the residual functions could be nonsmooth with respect to the unknown functions of endogenous variables it is a problem of nonparametric nonlinear instrumental variables iv estimation and a difficult nonlinear ill posed inverse problem with an unknown operator we first propose a penalized sieve minimum distance smd estimator of the unknown functions that are identified via the conditional moment models we then establish its consistency and convergence rate in strong metric allowing for possibly non compact function parameter spaces possibly non compact finite or infinite dimensional sieves with flexible lower semicompact or convex penalty or finite dimensional linear sieves without penalty under relatively low level sufficient conditions and for both mildly and severely ill posed problems we show that the convergence rates for the nonlinear ill posed inverse problems coincide with the known minimax optimal rates for the nonparametric mean iv regression we illustrate the theory by two important applications root n asymptotic normality of the plug in penalized smd estimator of a weighted average derivative of a nonparametric nonlinear iv regression and the convergence rate of a nonparametric additive quantile iv regression we also present a simulation study and an empirical estimation of a system of nonparametric quantile iv engel curves

the darling erdős theorem for sums of i i d random variables we obtain a general darling erd s type theorem for the maximum of appropriately normalized sums of i i d mean zero r v s with finite variances we infer that the darling erd s theorem holds in its classical formulation if and only ife x21 x t o loglogt 1 ast our method is based on an extension of the truncation techniques of feller 1946 to non symmetric r v s as a by product we are able to reprove fundamental results of feller 1946 dealing with lower and upper classes in the hartman wintner lil

nonparametric efficiency analysis a multivariate conditional quantile approach this paper focuses on nonparametric efficiency analysis based on robust estimation of partial frontiers in a complete multivariate setup multiple inputs and multiple outputs it introduces quantile efficiency scores a nonparametric estimator is proposed achieving strong consistency and asymptotic normality then if increases to one as a function of the sample size we recover the properties of the fdh estimator but our estimator is more robust to the perturbations in data since it attains a finite gross error sensitivity environmental variables can be introduced to evaluate efficiencies and a consistent estimator is proposed numerical examples illustrate the usefulness of the approach

nonparametric instrumental variables estimation of a quantile regression model we consider nonparametric estimation of a regression function that is identified by requiring a specified quantile of the regression error conditional on an instrumental variable to be zero the resulting estimating equation is a nonlinear integral equation of the first kind which generates an ill posed inverse problem the integral operator and distribution of the instrumental variable are unknown and must be estimated nonparametrically we show that the estimator is mean square consistent derive its rate of convergence in probability and give conditions under which this rate is optimal in a minimax sense the results of monte carlo experiments show that the estimator behaves well in finite samples

on eigenvalue pinching in positive ricci curvature we shall show that for manifolds with ric n 1 the radius is close to iff the n 1 st eigenvalue is close to n this extends results of cheng and croke which show that the diameter is close to iff the first eigenvalue is close to n we shall also give a new proof of an important theorem of colding to the effect that if the radius is close to then the volume is close to that of the sphere and the manifold is gromov hausdorff close to the sphere from work of cheeger and colding these conditions imply that the manifold is diffeomorphic to a sphere

local identification of nonparametric and semiparametric models in parametric nonlinear structural models a classical sufficient condition for local identification like fisher 1966 and rothenberg 1971 is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix we derive an analogous result for the nonparametric nonlinear structural models establishing conditions under which an infinite dimensional analog of the full rank condition is sufficient for local identification importantly we show that additional conditions are often needed in nonlinear nonparametric models to avoid nonlinearities overwhelming linear effects we give restrictions on a neighborhood of the true value that are sufficient for local identification we apply these results to obtain new primitive identification conditions in several important models including nonseparable quantile instrumental variable iv models and semiparametric consumption based asset pricing models

instrumental variable treatment of nonclassical measurement error models while the literature on nonclassical measurement error traditionally relies on the availability of an auxiliary data set containing correctly measured observations we establish that the availability of instruments enables the identification of a large class of nonclassical nonlinear errors in variables models with continuously distributed variables our main identifying assumption is that conditional on the value of the true regressors some measure of location of the distribution of the measurement error e g its mean mode or median is equal to zero the proposed approach relies on the eigenvalue eigenfunction decomposition of an integral operator associated with specific joint probability densities the main identifying assumption is used to index the eigenfunctions so that the decomposition is unique we propose a convenient sieve based estimator derive its asymptotic properties and investigate its finite sample behavior through monte carlo simulations

efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals this paper considers semiparametric efficient estimation ofconditional moment models with possibly nonsmooth residuals in unknown parametric components and unknown functions h of endogenous variables we show that 1 the penalized sieve minimum distance psmd estima tor can simultaneously achieve root n asymptotic normality ofand nonparametric optimal convergence rate of allowing for noncompact function parameter spaces 2 a simple weighted bootstrap procedure consistently estimates the limiting distribution of the psmd 3 the semi parametric efficiency bound formula of ai and chen 2003 remains valid for conditional models with nonsmooth residuals and the optimally weighted psmd estimator achieves the bound 4 the centered profiled optimally weighted psmd criterion is asymptotically chi square distributed we illustrate our theories using a partially linear quantile instrumental variables iv regression a monte carlo study and an empirical estimation of the shape invariant quantile iv engel curves

empirical likelihood estimation and consistent tests with conditional moment restrictions this paper is about efficient estimation and consistent tests of conditional moment restrictions we use unconditional moment restrictions based on splines or other approximating functions for this purpose empirical likelihood estimation is particularly appropriate for this setting because of its relatively low bias with many moment conditions we give conditions so that efficiency of estimators and consistency of tests is achieved as the number of restrictions grows with the sample size we also give results for generalized empirical likelihood generalized method of moments and nonlinear instrumental variable estimators

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

semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions abstract this paper computes the semiparametric efficiency bound for finite dimensional parameters identified by models of sequential moment restrictions containing unknown functions our results extend those of chamberlain 1992b and ai and chen 2003 for semiparametric conditional moment restrictions with identical information sets to the case of nested information sets and those of chamberlain 1992a and brown and newey 1998 for models of sequential moment restrictions without unknown functions to cases with unknown functions of possibly endogenous variables our results are applicable to semiparametric panel data models and two stage plug in problems as an important example we compute the efficiency bound for a weighted average derivative of a nonparametric instrumental variables regression npiv and find that simple plug in npiv estimators are not efficient we present an optimally weighted orthogonalized sieve minimum distance estimator that achieves the semiparametric efficiency bound

direct instrumental nonparametric estimation of inverse regression functions abstract this paper treats the estimation of the inverse g 1 of a monotonic function g satisfying e y g x w 0 where x w is continuously distributed using instrumental restrictions many parameters of interest in econometrics can be expressed as inverses of functions satisfying such a conditional moment as far as i know consistent estimators are available only if g x e y x which precludes endogenous models this and other technical concerns motivates a methodology for estimating g 1 in one step from the data when w contains components excluded from x the presented estimator achieves this objective by identifying g 1 as the solution of a nonlinear integral equation whose sample analog can be estimated nonparametrically the existence of a well behaved joint density function for x w produces an ill posed problem namely the solution is discontinuous in the data to solve this the estimator is regularized with the tikhonov technique if g 1 is smooth in a certain sense then the mse rate of convergence in a global metric is equal to n r 2 r 1 where is a continuous function with 0 0 and r 1 denotes the number of partial derivatives for the joint density of x w with respect to its second argument the analytical expression of depends on a link function characterizing the smoothness of g 1 this result holds for a broad class of link functions belonging to a suitable space

tikhonov regularization for nonparametric instrumental variable estimators abstract we study a tikhonov regularized tir estimator of a functional parameter identified by conditional moment restrictions in a linear model with both exogenous and endogenous regressors the nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by the norms of the parameter and its derivatives after showing its consistency in the sobolev norm and uniform consistency under an embedding condition we derive the expression of the asymptotic mean integrated square error and the rate of convergence the optimal value of the regularization parameter is characterized in two examples we illustrate our theoretical findings and the small sample properties with simulation results finally we provide an empirical application to estimation of an engel curve and discuss a data driven selection procedure for the regularization parameter

iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression this paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression we propose a regularized newton type iteration and establish convergence and convergence rate results a particular emphasis is on instrumental regression models where the usual conditional mean assumption is replaced by a stronger independence assumption we demonstrate for the case of a binary instrument that our approach allows the correct estimation of regression functions which are not identifiable with the standard model this is illustrated in computed examples with simulated data

higher moment estimators for linear regression models with errors in the variables abstract this paper proposes consistent instrumental variable estimators for linear regression models with errors in the variables that require no extraneous information these estimators are based on sample moments of order higher than two while similar estimators proposed previously in the literature seem to be quite erratic our experimental f findings suggest that our estimators perform better than ordinary least squares estimators in terms of root mean squared errors and also in terms of size of type i errors of standard tests in many typical situations of economic analyses tests for the presence of errors in the variables are also described

estimating derivatives in nonseparable models with limited dependent variables we present a simple way to estimate the effects of changes in a vector of observable variables x on a limited dependent variable y when y is a general nonseparable function of x and unobservables and x is independent of the unobservables we treat models in which y is censored from above below or both the basic idea is to first estimate the derivative of the conditional mean of y given x at x with respect to x on the uncensored sample without correcting for the effect of x on the censored population we then correct the derivative for the effects of the selection bias we discuss nonparametric and semiparametric estimators for the derivative we also discuss the cases of discrete regressors and of endogenous regressors in both cross section and panel data contexts

estimation of nonparametric conditional moment models with possibly nonsmooth generalized residuals this paper studies nonparametric estimation of conditional moment restrictions in which the generalized residual functions can be nonsmooth in the unknown functions of endogenous variables this is a nonparametric nonlinear instrumental variables iv problem we propose a class of penalized sieve minimum distance psmd estimators which are minimizers of a penalized empirical minimum distance criterion over a collection of sieve spaces that are dense in the infinite dimensional function parameter space some of the psmd procedures use slowly growing finite dimensional sieves with flexible penalties or without any penalty others use large dimensional sieves with lower semicompact and or convex penalties we establish their consistency and the convergence rates in banach space norms such as a sup norm or a root mean squared norm allowing for possibly noncompact infinite dimensional parameter spaces for both mildly and severely ill posed nonlinear inverse problems our convergence rates in hilbert space norms such as a root mean squared norm achieve the known minimax optimal rate for the nonparametric mean iv regression we illustrate the theory with a nonparametric additive quantile iv regression we present a simulation study and an empirical application of estimating nonparametric quantile iv engel curves

gmm estimators with improved finite sample properties using principal components of the weighting matrix with an application to the dynamic panel data model gmm estimators have poor finite sample properties in highly overidentified models with many moment conditions the optimal weighting matrix is poorly estimated we suggest using principal components of the weighting matrix this effectively drops some of the moment conditions our simulations done in the context of the dynamic panel data model show that the resulting gmm estimator has better finite sample properties than the usual two step gmm estimator in the sense of smaller bias and more reliable standard errors

injectivity of a class of integral operators with compactly supported kernels abstract injectivity of integral operators is related to completeness conditions of their corresponding kernel functions completeness provides a useful way of obtaining nonparametric identification in various models including nonparametric regression models with instrumental variables nonclassical measurement error models and auction models etc however the condition is quite abstract for empirical work and lacks a proper economic interpretation we rely on known results regarding the volterra equation to provide sufficient conditions for completeness conditions for densities with compact support our conditions include various smoothness assumptions and monotonously moving support assumptions on the kernel function of the operator we apply our results to establish nonparametric identification in nonparametric iv regression models nonclassical measurement error models and auction models with an accessible interpretation and without specific functional form restrictions

regularization of nonparametric frontier estimators in production theory and efficiency analysis we estimate the production frontier the locus of the maximal attainable level of an output the production given a set of inputs the production factors in other setups we estimate rather an input or cost frontier the minimal level of the input cost attainable for a given set of outputs goods or services produced in both cases the problem can be viewed as estimating a surface under shape constraints monotonicity in this paper we derive the theory of an estimator of the frontier having an asymptotic normal distribution it is based on the order mpartial frontier where we let the ordermto converge to infinity when n but at a slow rate the final estimator is then corrected for its inherent bias we thus can view our estimator as a regularized frontier in addition the estimator is more robust to extreme values and outliers than the usual nonparametric frontier estimators like fdh and than the unregularized order mn estimator of cazals et al 2002 converging to the frontier with a weibull distribution if m n fast enough when n the performances of our estimators are evaluated in finite samples and compared to other estimators through some monte carlo experiments showing a better behavior in terms of robustness bias mse and achieved coverage of the resulting confidence intervals the practical implementation and the robustness properties are illustrated through simulated data sets but also with a real data set

nonparametric instrumental variable estimation of structural quantile effects we study the asymptotic distribution of tikhonov regularized estimation of quantile structural effects implied by a nonseparable model the nonparametric instrumental variable estimator is based on a minimum distance principle we show that the min imum distance problem without regularization is locally ill posed and we consider penalization by the norms of the parameter and its derivatives we derive pointwise asymptotic normality and develop a consistent estimator of the asymptotic variance we study the small sample properties via simulation results and provide an empirical illustration of estimation of nonlinear pricing curves for telecommunications services in the united states

identification in nonparametric simultaneous equations models this paper provides conditions for identification of functionals in nonparametric simultaneous equations models with nonadditive unobservable random terms the conditions are derived from a characterization of observational equivalence between models we show that in the models considered observational equivalence can be characterized by a restriction on the rank of a matrix the use of the new results is exemplified by deriving previously known results about identification in parametric and nonparametric models as well as new results a stylized method for analyzing identification which is useful in some situations is also presented

examples of l2 complete and boundedly complete distributions abstract completeness and bounded completeness conditions are used increasingly in econometrics to obtain nonparametric identification in a variety of models from nonparametric instrumental variable regression to non classical measurement error models however distributions that are known to be complete or boundedly complete are somewhat scarce in this paper we consider an l 2 completeness condition that lies between completeness and bounded completeness we construct broad nonparametric classes of distributions that are l 2 complete and boundedly complete the distributions can have any marginal distributions and a wide range of strengths of dependence examples of l 2 incomplete distributions also are provided

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

exact convergence rates for the bounded law of the iterated logarithm in hilbert space in a previous paper we obtained upper and lower class type results refining the bounded lil for sums of iid hilbert space valued mean zero random variables whose covariance operators satisfy certain regularity assumptions we now establish precise convergence rates for the bounded lil in the non regular case it turns out that the almost sure behavior in this case is entirely different from the behavior in the previous situation

uniform confidence bands for functions estimated nonparametrically with instrumental variables abstract this paper is concerned with developing uniform confidence bands for functions estimated nonparametrically with instrumental variables we show that a sieve nonparametric instrumental variables estimator is pointwise asymptotically normally distributed the asymptotic normality result holds in both mildly and severely ill posed cases we present methods to obtain a uniform confidence band and show that the bootstrap can be used to obtain the required critical values monte carlo experiments illustrate the finite sample performance of the uniform confidence band

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

a regularization approach to the many instruments problem abstract this paper focuses on the estimation of a finite dimensional parameter in a linear model where the number of instruments is very large or infinite in order to improve the small sample properties of standard instrumental variable iv estimators we propose three modified iv estimators based on three different ways of inverting the covariance matrix of the instruments these inverses involve a regularization or smoothing parameter it should be stressed that no restriction on the number of instruments is needed and that all the instruments are used in the estimation we show that the three estimators are asymptotically normal and attain the semiparametric efficiency bound higher order analysis of the mse reveals that the bias of the modified estimators does not depend on the number of instruments finally we suggest a data driven method for selecting the regularization parameter interestingly our regularization techniques lead to a consistent nonparametric estimation of the optimal instrument

posterior consistency of nonparametric conditional moment restricted models this paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite dimensional parameter g0 we estimate it in a quasi bayesian way based on the limited information likelihood and investigate the impact of three types of priors on the posterior consistency i truncated prior priors supported on a bounded set ii thin tail prior a prior that has very thin tail outside a growing bounded set and iii normal prior with nonshrinking variance in addition g0 is allowed to be only partially identified in the frequentist sense and the parameter space does not need to be compact the posterior is regularized using a slowly growing sieve dimension and it is shown that the posterior converges to any small neighborhood of the identified region we then apply our results to the nonparametric instrumental regression model finally the posterior consistency using a random sieve dimension parameter is studied

geometric and spectral estimates based on spectral ricci curvature assumptions we obtain a bonnet myers theorem under a spectral condition a closed riemannian manifold mn g for which the lowest eigenvalue of the ricci tensor is such that the schr odinger operator n 2 is positive has finite fundamental group as a continuation of our earlier results we obtain isoperimetric inequalities from a kato condition on the ricci curvature furthermore we obtain the kato condition for the ricci curvature under purely geometric assumptions

sieve wald and qlr inferences on semi nonparametric conditional moment models this paper considers inference on functionals of semi nonparametric conditional moment restrictions with possibly nonsmooth generalized residuals which include all of the nonlinear nonparametric instrumental variables iv as special cases these models are often ill posed and hence it is difficult to verify whether a possibly nonlinear functional is root n estimable or not we provide computationally simple unified inference procedures that are asymptotically valid regardless of whether a functional is root n estimable or not we establish the following new useful results 1 the asymptotic normality of a plug in penalized sieve minimum distance psmd estimator of a possibly nonlinear functional 2 the consistency of simple sieve variance estimators for the plug in psmd estimator and hence the asymptotic chi square distribution of the sieve wald statistic 3 the asymptotic chi square distribution of an optimally weighted sieve quasi likelihood ratio qlr test under the null hypothesis 4 the asymptotic tight distribution of a non optimally weighted sieve qlr statistic under the null 5 the consistency of generalized residual bootstrap sieve wald and qlr tests 6 local power properties of sieve wald and qlr tests and of their bootstrap versions 7 asymptotic properties of sieve wald and sqlr for functionals of increasing dimension simulation studies and an empirical illustration of a nonparametric quantile iv regression are presented

testing for separability in structural equations abstract separability is an important feature of structural equations as it implies the absence of unobservable heterogeneity of effects and has significant implications for identification and efficiency of estimation this paper provides a nonparametric test for separability in structural equations the test is based on a conditional independence test recently developed by huang et al 2013 building on consistent procedures of bierens 1982 1990 and stinchcombe and white 1998 the test is easy to implement and achieves n local power we apply our test to study interest rate elasticities of loan demand in microfinance and the impact of education on wages

identification in nonseparable models weak nonparametric restrictions are developed sufficient to identify the values of derivatives of structural functions in which latent random variables are nonseparable these derivatives can exhibit stochastic variation in a microeconometric context this allows the impact of a policy intervention as measured by the value of a structural derivative to vary across people who are identical as measured by covariates when the restrictions are satisfied quantiles of the distribution of a policy impact across people can be identified the identification restrictions are local in the sense that they are specific to the values of the covariates and the specific quantiles of latent variables at which identification is sought the conditions do not include the commonly required independence of latent variables and covariates they include local versions of the classical rank and order conditions and local quantile insensitivity conditions values of structural derivatives are identified by functionals of quantile regression functions and can be estimated using the same functionals applied to estimated quantile regression functions

nonparametric instrumental regression the focus of this paper is the nonparametric estimation of an instrumental regression function f defined by conditional moment restrictions that stem from a structural econometric model e y f z w 0 and involve endogenous variables y and z and instruments w the function f is the solution of an ill posed inverse problem and we propose an estimation procedure based on tikhonov regularization the paper analyzes identification and overidentification of this model and presents asymptotic properties of the estimated nonparametric instrumental regression function

nonparametric estimation of nonadditive random functions we present estimators for nonparametric functions that are nonadditive in unobservable random terms the distributions of the unobservable random terms are assumed to be unknown we show that when a nonadditive nonparametric function is strictly monotone in an unobservable random term and it satisfies some other properties that may be implied by economic theory such as homogeneity of degree one or separability the function and the distribution of the unobservable random term are identified we also present convenient normalizations to use when the properties of the function other than strict monotonicity in the unobservable random term are unknown the estimators for the nonparametric function and for the distribution of the unobservable random term are shown to be consistent and asymptotically normal we extend the results to functions that depend on a multivariate random term the results of a limited simulation study are presented

a discontinuity test for identification in triangular nonseparable models this paper presents a test for the validity of control variable approaches to identification in triangular nonseparable models assumptions commonly imposed to justify such methods include full independence of instruments and disturbances and existence of a reduced form that is strictly monotonic in a scalar disturbance we show that if the data has a particular structure namely that the distribution of the endogenous variable has a mass point at the lower or upper boundary of its support validity of the control variable approach implies a continuity condition on an identified function which can be tested empirically

on the rate of convergence in strassen s law of the iterated logarithm let w t be a standard wiener process and let l be the compact class figuring in strassen s law of the iterated logarithm we investigate the rate of convergence to zero of the variable mathop inf limits f in mathfrak l text mathop text sup limits text 0 leqq x leqq 1 text w xt 2t log log t frac 1 2 f x it is shown that as t log log t belongs to the upper class of this variable if 2 3

penalized sieve gel for weighted average derivatives of nonparametric quantile iv regressions abstract this paper considers estimation and inference for a weighted average derivative wad of a nonparametric quantile instrumental variables regression npqiv npqiv is a non separable and nonlinear ill posed inverse problem which might be why there is no published work on the asymptotic properties of any estimator of its wad we first characterize the semiparametric efficiency bound for a wad of a npqiv which unfortunately depends on an unknown conditional derivative operator and hence an unknown degree of ill posedness making it difficult to know if the information bound is singular or not in either case we propose a penalized sieve generalized empirical likelihood gel estimation and inference procedure which is based on the unconditional wad moment restriction and an increasing number of unconditional moments that are implied by the conditional npqiv restriction where the unknown quantile function is approximated by a penalized sieve under some regularity conditions we show that the self normalized penalized sieve gel estimator of the wad of a npqiv is asymptotically standard normal we also show that the quasi likelihood ratio statistic based on the penalized sieve gel criterion is asymptotically chi square distributed regardless of whether or not the information bound is singular

identification of marginal effects in nonseparable models without monotonicity nonseparable models do not impose any type of additivity between the unobserved part and the observable regressors and are therefore ideal for many economic applications to identify these models using the entire joint distribution of the data as summarized in regression quantiles monotonicity in unobservables has frequently been assumed this paper establishes that in the absence of monotonicity the quantiles identify local average structural derivatives of nonseparable models

an iv model of quantile treatment effects the ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications however in observational studies the variables of interest e g education prices are often endogenous making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes in order to address this problem we develop a model of quantile treatment effects qte in the presence of endogeneity and obtain conditions for identification of the qte without functional form assumptions the principal feature of the model is the imposition of conditions that restrict the evolution of ranks across treatment states this feature allows us to overcome the endogeneity problem and recover the true qte through the use of instrumental variables the proposed model can also be equivalently viewed as a structural simultaneous equation model with nonadditive errors where qte can be interpreted as the structural quantile effects sqe

choosing the number of instruments properties of instrumental variable estimators are sensitive to the choice of valid instruments even in large cross section applications in this paper we address this problem by deriving simple mean square error criteria that can be minimized to choose the instrument set we develop these criteria for two stage least squares 2sls limited information maximum likelihood liml and a bias adjusted version of 2sls b2sls we give a theoretical derivation of the mean square error and show optimality in monte carlo experiments we find that the instrument choice generally yields an improvement in performance also in the angrist and krueger 1991 returns to education application when the instrument set is chosen in the way we consider it turns out that both 2sls and liml give similar large returns to education

overidentification in regular models in the unconditional moment restriction model of hansen specification tests and more efficient estimators are both available whenever the number of moment restrictions exceeds the number of parameters of interest we show that a similar relationship between potential refutability of a model and existence of more efficient estimators is present in much broader settings specifically a condition we name local overidentification is shown to be equivalent to both the existence of specification tests with nontrivial local power and the existence of more efficient estimators of some smooth parameters in general semi nonparametric models under our notion of local overidentification various locally nontrivial specification tests such as hausman tests incremental sargan tests or optimally weighted quasi likelihood ratio tests naturally extend to general semi nonparametric settings we further obtain simple characterizations of local overidentification for general models of nonparametric conditional moment restrictions with possibly different conditioning sets the results are applied to determining when semi nonparametric models with endogeneity are locally testable and when nonparametric plug in and semiparametric two step gmm estimators are semiparametrically efficient examples of empirically relevant semi nonparametric structural models are presented

adaptive nonparametric instrumental variables estimation empirical choice of the regularization parameter abstract in nonparametric instrumental variables estimation the mapping that identifies the function of interest g is discontinuous and must be regularized to permit consistent estimation the optimal regularization parameter depends on population characteristics that are unknown in applications this paper presents a theoretically justified empirical method for choosing the regularization parameter in series estimation the method adapts to the unknown smoothness of g and other unknown functions the resulting estimator of g converges at least as fast as the optimal rate multiplied by log n 1 2 the asymptotic integrated mean square error aimse of the estimator is within a specified factor of the optimal aimse

a note on the law of the iterated logarithm in hilbert space kuelbs 1975 established a kolmogorov erdos petrowski type integral test for lower and upper classes in the law of the iterated logarithm for sums of i i d hilbert space valued gaussian mean zero random variables we show that this integral test remains valid for sums of i i d pregaussian mean zero random variables satisfying an additional very mild assumption

hierarchical spline models for conditional quantiles and the demand for electricity abstract methods for estimating nonparametric models for conditional quantiles are suggested based on the regression quantile methods of koenker and bassett spline parameterizations of the conditional quantile functions are used the methods are illustrated by estimating hierarchical models for household electricity demand using data from the chicago metropolitan area the empirical results show that lower quantiles of demand base load vary only slightly across residential households this variability is difficult to explain using household characteristics however upper quantiles of the demand distribution vary considerably and are systematically related to household characteristics and appliance ownership the implications of analyzing mean demand behavior rather than various quantiles of the distribution of demand are also discussed

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail