instrumental variable estimation of nonlinear models with nonclassical measurement error using control variables we consider nonlinear models with an independent variable that is measured with error the measurement error can be correlated with the true value i e the measurement error is allowed to be nonclassical we show that we can use a control variate estimator to estimate the parameters of interest if we are prepared to make an assumption of the joint distribution of the rst stage

nonparametric estimation of distributional policy effects this paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest in contrast to other methods we do not restrict attention to the effect on the mean in particular our method can be used to conduct inference on the change of the distribution function as a whole its moments and quantiles inequality measures such as the lorenz curve or gini coefficient and to test for stochastic dominance the practical applicability of our procedure is illustrated via a simulation study and an empirical example

semi parametric single index panel data models with interactive fixed effects theory and practice abstract in this paper we propose a single index panel data model with unobserved multiple interactive fixed effects this model has the advantages of being flexible and of being able to allow for common shocks and their heterogeneous impacts on cross sections thus making it suitable for the investigation of many economic issues the asymptotic theories are established accordingly our monte carlo simulations show that our methodology works well for large n and t cases in our empirical application we illustrate our model by analysing the returns to scale of large commercial banks in the u s

efficiency bounds for estimating linear functionals of nonparametric regression models with endogenous regressors abstract let y x e where is unknown and e e x 0 with positive probability but there exist instrumental variables w such that e e w 0 w p 1 it is well known that such nonparametric regression models are generally ill posed in the sense that the map from the data to is not continuous in this paper we derive the efficiency bounds for estimating certain linear functionals of without assuming itself to be identified

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

informational content of special regressors in heteroskedastic binary response models we quantify the informational content of special regressors in heteroskedastic binary response models with median independent or conditionally symmetric errors based on lewbel 1998 a special regressor is additively separable in the latent payoff and conditionally independent from the error term we find that with median independent errors a special regressor does not increase the identifying power by a criterion in manski 1988 or lead to positive fisher information for the coefficients even though it does help recover the average structural function with conditionally symmetric errors a special regressor improves the identifying power and the information for coefficients is positive under mild conditions we propose two estimators for binary response models with conditionally symmetric errors and special regressors

doubly robust estimation of the local average treatment effect curve we consider estimation of the causal effect of a binary treatment on an outcome conditionally on covariates from observational studies or natural experiments in which there is a binary instrument for treatment we describe a doubly robust locally efficient estimator of the parameters indexing a model for the local average treatment effect conditionally on covariates v when randomization of the instrument is only true conditionally on a high dimensional vector of covariates x possibly bigger than v we discuss the surprising result that inference is identical to inference for the parameters of a model for an additive treatment effect on the treated conditionally on v that assumes no treatment instrument interaction we illustrate our methods with the estimation of the local average effect of participating in 401 k retirement programs on savings by using data from the us census bureau s 1991 survey of income and program participation

root n consistent semiparametric estimators of a dynamic panel sample selection model abstract this paper considers the problem of identification and estimation in panel data sample selection models with a binary selection rule when the latent equations contain possibly predetermined variables lags of the dependent variables and unobserved individual effects the selection equation contains lags of the dependent variables from both the latent and the selection equations as well as other possibly predetermined variables relative to the latent equations we derive a set of conditional moment restrictions that are then exploited to construct a three step sieve estimator for the parameters of the main equation including a nonparametric estimator of the sample selection term in the second step the unknown parameters of the selection equation are consistently estimated using a transformation approach in the spirit of berkson s minimum chi square sieve method and a first step kernel estimator for the selection probability this second step estimator is of interest in its own right it can be used to semiparametrically estimate a panel data binary response model with a nonparametric individual specific effect without making any other distributional assumptions we show that both estimators second and third stage are n consistent and asymptotically normal

testing the drift diffusion model the drift diffusion model ddm is a model of sequential sampling with diffusion signals where the decision maker accumulates evidence until the process hits either an upper or lower stopping boundary and then stops and chooses the alternative that corresponds to that boundary in perceptual tasks the drift of the process is related to which choice is objectively correct whereas in consumption tasks the drift is related to the relative appeal of the alternatives the simplest version of the ddm assumes that the stopping boundaries are constant over time more recently a number of papers have used nonconstant boundaries to better fit the data this paper provides a statistical test for ddms with general nonconstant boundaries as a by product we show that the drift and the boundary are uniquely identified we use our condition to nonparametrically estimate the drift and the boundary and construct a test statistic based on finite samples

local partitioned regression in this paper we introduce a kernel based estimation principle for nonparametric models named local partitioned regression lpr this principle is a nonparametric generalization of the familiar partition regression in linear models it has several key advantages first it generates estimators for a very large class of semi and nonparametric models a number of examples that are particularly relevant for economic applications will be discussed in this paper this class contains the additive partially linear and varying coefficient models as well as several other models that have not been discussed in the literature second lpr based estimators achieve optimality criteria they have optimal speed of convergence and are oracle efficient moreover they are simple in structure widely applicable and computationally inexpensive a monte carlo simulation highlights these advantages

semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables this paper provides estimators of discrete choice models including binary ordered and multinomial response choice models the estimators closely resemble ordinary and two stage least squares the distribution of the model s latent variable error is unknown and may be related to the regressors e g the model could have errors that are heteroscedastic or correlated with regressors the estimator does not require numerical searches even for multinomial choice for ordered and binary choice models the estimator is root n consistent and asymptotically normal a consistent estimator of the conditional error distribution is also provided

semiparametric crb and slepian bangs formulas for complex elliptically symmetric distributions the main aim of this paper is to extend the semiparametric inference methodology recently investigated for real elliptically symmetric res distributions to complex elliptically symmetric ces distributions the generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data moreover the ces distributions has been widely recognized as a valuable and general model to statistically describe the non gaussian behaviour of datasets originated from a wide variety of physical measurement processes the paper is divided in two parts in the first part a closed form expression of the constrained semiparametric cramer rao bound cscrb for the joint estimation of complex mean vector and complex scatter matrix of a set of ces distributed random vectors is obtained by exploiting the so called wirtinger or mathbb c mathbb r calculus the second part deals with the derivation of the semiparametric version of the slepian bangs formula in the context of the ces model specifically the proposed semiparametric slepian bangs ssb formula provides us with a useful and ready to use expression of the semiparametric fisher information matrix sfim for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a ces distributed vector in the presence of unknown nuisance density generator furthermore we show how to exploit the derived ssb formula to obtain the semiparametric counterpart of the stochastic crb for direction of arrival doa estimation under a random signal model assumption simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications

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

estimation of a nonlinear panel data model with semiparametric individual effects abstract this paper investigates identification and estimation of a class of nonlinear panel data single index models the model allows for unknown time specific link functions and semiparametric specification of the individual specific effects we develop an estimator for the parameters of interest and propose a powerful new kernel based modified backfitting algorithm to compute the estimator we derive uniform rates of convergence results for the estimators of the link functions and show the estimators of the finite dimensional parameters are root n consistent with a gaussian limiting distribution we study the small sample properties of the estimator via monte carlo techniques

efficiency of weighted average derivative estimators and index models weighted average derivatives are useful parameters for semiparametric index models and nonparametric demand analysis this paper gives efficiency results for average derivative estimators including formulating estimators that have high efficiency our analysis is carried out in three steps first we derive the efficiency bound for weighted average derivatives of conditional location functionals such as the conditional mean and median second we derive the efficiency bound for semiparametric index models where the location measure depends only on indices or linear combinations of the regressors third we compare the bound for index models with the asymptotic variance of weighted average derivative estimators of the index coefficients we characterize the form of the optimal weight function when the distribution of the regressors is elliptically symmetric in more general cases we discuss how to combine estimators with different weight functions to achieve efficiency we derive a general condition for approximate efficiency of pooled minimum chi square estimators for index model coefficients based on weighted average derivatives finally we discuss ways of selecting the type and number of weighting functions to achieve high efficiency

estimation of semiparametric models when the criterion function is not smooth we provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated our results extend existing theories such as those of pakes and pollard 1989 andrews 1994a and newey 1994 we also show that bootstrap provides asymptotically correct confidence regions for the finite dimensional parameters we apply our results to two examples a hit rate and a partially linear median regression with some endogenous regressors

estimation of copula based semiparametric time series models this paper studies the estimation of a class of copula based semiparametric stationary markov models these models are characterized by nonparametric marginal distributions and parametric copula functions while the copulas capture all the scale free temporal dependence of the processes simple estimators of the marginal distribution and the copula parameter are provided and their asymptotic properties are established under easily verifiable conditions these results are used to obtain root n consistent and asymptotically normal estimators of important features of the transition distribution such as the nonlinear conditional moments and conditional quantiles the semiparametric conditional quantile estimators are automatically monotonic across quantiles which is attractive for portfolio conditional value at risk calculations

optimal bandwidth choice for density weighted averages abstract this paper characterizes the optimal bandwidth value for estimating density weighted averages statistics that arise in semiparametric estimation methods for index models and models of selected samples based on nonparametric kernel estimators the optimal bandwidth is derived by minimizing the leading terms of mean squared error of the density weighted average the optimal bandwidth formulation is developed by comparison to the optimal pointwise bandwidth of a naturally associated nonparametric estimation problem highlighting the role of sample size and the structure of nonparametric estimation bias the methods are illustrated by estimators of average density density weighted average derivatives and conditional covariances and bandwidth values are calculated for normal designs a simple plug in estimator for the optimal bandwidth is proposed finally the optimal bandwidth for estimating ratios of density weighted averages is derived showing that the earlier optimal formulae can be implemented directly using naturally defined residual values

merging multiple longitudinal studies with study specific missing covariates a joint estimating function approach merging multiple datasets collected from studies with identical or similar scientific objectives is often undertaken in practice to increase statistical power this article concerns the development of an effective statistical method that enables to merge multiple longitudinal datasets subject to various heterogeneous characteristics such as different follow up schedules and study specific missing covariates e g covariates observed in some studies but missing in other studies the presence of study specific missing covariates presents great statistical methodology challenge in data merging and analysis we propose a joint estimating function approach to addressing this challenge in which a novel nonparametric estimating function constructed via splines based sieve approximation is utilized to bridge estimating equations from studies with missing covariates to those with fully observed covariates under mild regularity conditions we show that the proposed estimator is consistent and asymptotically normal we evaluate finite sample performances of the proposed method through simulation studies in comparison to the conventional multiple imputation approach our method exhibits smaller estimation bias we provide an illustrative data analysis using longitudinal cohorts collected in mexico city to assess the effect of lead exposures on children s somatic growth

estimation and testing for partially linear single index models in partially linear single index models we obtain the semiparametrically efficient profile least squares estimators of regression coefficients we also employ the smoothly clipped absolute deviation penalty scad approach to simultaneously select variables and estimate regression coefficients we show that the resulting scad estimators are consistent and possess the oracle property subsequently we demonstrate that a proposed tuning parameter selector bic identifies the true model consistently finally we develop a linear hypothesis test for the parametric coefficients and a goodness of fit test for the nonparametric component respectively monte carlo studies are also presented

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

efficient estimation in multi phase case control studies in this paper we discuss the analysis of multi phase or multi stage case control studies and present an efficient semiparametric maximum likelihood approach that unifies and extends earlier work including the seminal case control paper by prentice pyke 1979 work by breslow cain 1988 scott wild 1991 breslow holubkov 1997 and others the theoretical derivations apply to arbitrary binary regression models but we present results for logistic regression and show that the approach can be implemented by including additional intercept terms in the logistic model and then making some simple corrections to the score and information equations used in a newton raphson or fisher scoring maximization of the prospective loglikelihood

characterization of the asymptotic distribution of semiparametric m estimators this paper develops a concrete formula for the asymptotic distribution of two step possibly non smooth semiparametric m estimators under general misspecification our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature the first stage nonparametric estimation may depend on finite dimensional parameters we characterize 1 conditions under which the first stage estimation of nonparametric components do not affect the asymptotic distribution 2 conditions under which the asymptotic distribution is affected by the derivatives of the first stage nonparametric estimator with respect to the finite dimensional parameters and 3 conditions under which one can allow non smooth objective functions our framework is illustrated by applying it to three examples 1 profiled estimation of a single index quantile regression model 2 semiparametric least squares estimation under model misspecification and 3 a smoothed matching estimator 2010 elsevier b v all rights reserved

semiparametric latent variable model estimation with endogenous or mismeasured regressors a simple root n consistent asymptotically normal semiparametric estimator of the coefficient vector b in the latent variable specification y l f b x e is constructed the distribution of e is unknown and may be correlated with x or be conditionally heteroscedastic e g x can contain measurement error the function l can also be unknown the identification assumption is that e is uncorrelated with instruments u and that the conditional distribution of e given x and u does not depend on one of the regressors which has some special properties extensions to more general latent variable specifications are provided

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

all linear and integer programs are slim 3 way transportation programs we show that any rational convex polytope is polynomial time representable as a 3 way line sum transportation polytope of slim r c 3 format this universality theorem has important consequences for linear and integer programming and for confidential statistical data disclosure we provide a polynomial time embedding of arbitrary linear programs and integer programs in such slim transportation programs and in bitransportation programs our construction resolves several standing problems on 3 way transportation polytopes for example it demonstrates that unlike the case of 2 way contingency tables the range of values an entry can attain in any slim 3 way contingency table with specified 2 margins can contain arbitrary gaps our smallest such example has format 6 4 3 our construction provides a powerful automatic tool for studying concrete questions about transportation polytopes and contingency tables for example it automatically provides new proofs for some classical results including a well known real feasible but integer infeasible 6 4 3 transportation polytope of m vlach and bitransportation programs where any feasible bitransportation must have an arbitrarily large prescribed denominator

quasi oracle estimation of heterogeneous treatment effects flexible estimation of heterogeneous treatment effects lies at the heart of many statistical challenges such as personalized medicine and optimal resource allocation in this paper we develop a general class of two step algorithms for heterogeneous treatment effect estimation in observational studies we first estimate marginal effects and treatment propensities in order to form an objective function that isolates the causal component of the signal then we optimize this data adaptive objective function our approach has several advantages over existing methods from a practical perspective our method is flexible and easy to use in both steps we can use any loss minimization method e g penalized regression deep neural networks or boosting moreover these methods can be fine tuned by cross validation meanwhile in the case of penalized kernel regression we show that our method has a quasi oracle property even if the pilot estimates for marginal effects and treatment propensities are not particularly accurate we achieve the same error bounds as an oracle who has a priori knowledge of these two nuisance components we implement variants of our approach based on penalized regression kernel ridge regression and boosting in a variety of simulation setups and find promising performance relative to existing baselines

nonparametric iv estimation of local average treatment effects with covariates in this paper nonparametric instrumental variable estimation of local average treatment effects late is extended to incorporate covariates estimation of late is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models including covariates in the estimation of late is necessary when the instrumental variable itself is confounded such that the iv assumptions are valid only conditional on covariates previous approaches to handle covariates in the estimation of late relied on parametric or semiparametric methods in this paper a nonparametric estimator for the estimation of late with covariates is suggested that is root n asymptotically normal and efficient

causal inference in outcome dependent two phase sampling designs summary we consider estimation of the causal effect of a treatment on an outcome from observational data collected in two phases in the first phase a simple random sample of individuals is drawn from a population on these individuals information is obtained on treatment outcome and a few low dimensional covariates these individuals are then stratified according to these factors in the second phase a random subsample of individuals is drawn from each stratum with known stratum specific selection probabilities on these individuals a rich set of covariates is collected in this setting we introduce five estimators simple inverse weighted simple doubly robust enriched inverse weighted enriched doubly robust locally efficient we evaluate the finite sample performance of these estimators in a simulation study we also use our methodology to estimate the causal effect of trauma care on in hospital mortality by using data from the national study of cost and outcomes of trauma

minimum distance from independence estimation of nonseparable instrumental variables models abstract i develop a semiparametric minimum distance from independence estimator for a nonseparable instrumental variables model an independence condition identifies the model for many types of discrete and continuous instruments the estimator is taken as the parameter value that most closely satisfies this independence condition implementing the estimator requires a quantile regression of the endogenous variables on the instrument so the procedure is two step with a finite or infinite dimensional nuisance parameter in the first step i prove consistency and establish asymptotic normality for a parametric but flexibly nonlinear outcome equation the consistency of the nonparametric bootstrap is also shown i illustrate the use of the estimator by estimating the returns to schooling using data from the 1979 national longitudinal survey

instrumental variable estimation of nonlinear errors in variables models this paper establishes that instruments enable the identification of nonparametric regression models in the presence of measurement error by providing a closed form solution for the regression function in terms of fourier transforms of conditional expectations of observable variables for parametrically specified regression functions we propose a root n consistent and asymptotically normal estimator that takes the familiar form of a generalized method of moments estimator with a plugged in nonparametric kernel density estimate both the identification and the estimation methodologies rely on fourier analysis and on the theory of generalized functions the finite sample properties of the estimator are investigated through monte carlo simulations

semiparametric estimation of a simultaneous game with incomplete information abstract this paper studies the problem of estimating the normal form payoff parameters of a simultaneous discrete game where the realization of such payoffs is not common knowledge the paper contributes to the existing literature in two ways first by making a comparison with the complete information case it formally describes a set of conditions under which allowing for private information in payoffs facilitates the identification of various features of the game second focusing on the incomplete information case it presents an estimation procedure based on the equilibrium properties of the game that relies on weak semiparametric assumptions and relatively flexible information structures which allow players to condition their beliefs on signals whose exact distribution function is unknown to the researcher the proposed estimators recover unobserved beliefs by solving a semiparametric sample analog of the population bayesian nash equilibrium conditions the asymptotic features of such estimators are studied for the case in which the distribution of unobserved shocks is known and the case in which it is unknown in both instances equilibrium uniqueness is assumed to hold only in a neighborhood of the true parameter value and for a subset z of realizations of the signals multiple equilibria are allowed elsewhere in the parameter space and no equilibrium selection theory is involved extensions to games where beliefs are conditioned on unobservables as well as general games with many players and actions are also discussed an empirical application of a simple capital investment game is included

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

local indirect least squares and average marginal effects in nonseparable structural systems we study the scope of local indirect least squares lils methods for nonparametrically estimating average marginal effects of an endogenous cause x on a response y in triangular structural systems that need not exhibit linearity separability or monotonicity in scalar unobservables one main finding is negative in the fully nonseparable case lils methods cannot recover the average marginal effect lils methods can nevertheless test the hypothesis of no effect in the general nonseparable case we provide new nonparametric asymptotic theory treating both the traditional case of observed exogenous instruments z and the case where one observes only error laden proxies for z

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

fitting binary regression models with case augmented samples summary in a case augmented study measurements on a random sample from a population are augmented by information from an independent sample of cases that is units with some characteristic of interest we show that inferences about the effect of the covariates on the probability of being a case can be made by fitting a modified prospective likelihood we also show that this procedure is fully efficient

model selection in the presence of incidental parameters this paper considers model selection in panels where incidental parameters are present primary interest centers on selecting a model that best approximates the underlying structure involving parameters that are common within the panel it is well known that conventional model selection procedures are often inconsistent in panel models and this can be so even without nuisance parameters modifications are then needed to achieve consistency new model selection information criteria are developed here that use either the kullback leibler information criterion based on the profile likelihood or the bayes factor based on the integrated likelihood with a bias reducing prior these model selection criteria impose heavier penalties than those associated with standard information criteria such as aic and bic the additional penalty which is data dependent properly reflects the model complexity arising from the presence of incidental parameters a particular example is studied in detail involving lag order selection in dynamic panel models with fixed effects the new criteria are shown to control for over under selection probabilities in these models and lead to consistent order selection criteria

three stage semi parametric inference control variables and differentiability abstract we show the usefulness of the path derivative calculations that were introduced in econometrics by newey 1994 for multi step semi parametric estimators these estimators estimate a finite dimensional parameter using moment conditions that depend on nonparametric regressions on observed and estimated regressors that are estimated in the second and first step of the estimation procedure respectively our earlier paper showed that newey s calculations can be extended to three step estimators in the current paper we consider the control variable cv estimator and related statistics in semi parametric econometric models with non separable errors and regressors that are correlated with these errors non separable econometric models with endogenous regressors are often identified by average moment restrictions that average over control variables and these control variables are estimated in a first stage by non parametric regression we study aspects of inference for such estimators where we focus on a finite dimensional parameter vector or statistic the asymptotic distribution and a closed form expression for the asymptotic variance of the cv estimator were not available until now our path derivative calculations are much simpler than the derivation of the asymptotic distribution by a stochastic expansion that is particularly complicated for multi step semi parametric estimators we also consider just and overidentification of the parameters and we propose a diagnostic test for overidentifying restrictions in models with non separable errors and endogenous regressors finally the path derivative calculation breaks down if the moment condition is not differentiable in an example we show that non differentiability is associated with irregular behavior of the estimator

identification and n consistent estimation of a nonlinear panel data model with correlated unobserved effects abstract this paper investigates identification and root n consistent estimation of a class of single index panel data models in which the link function is unknown the unobserved individual effects may be correlated with all the explanatory variables and all the explanatory variables may be predetermined we propose two sets of sufficient conditions one in which link function is assumed to be strictly increasing and the other in which it is not we propose simple kernel based estimators for the models and derive consistency and asymptotic normality results for the proposed estimators finally we present results of two monte carlo studies of the estimators

generalized partially linear single index model for zero inflated count data count data often arise in biomedical studies while there could be a special feature with excessive zeros in the observed counts the zero inflated poisson model provides a natural approach to accounting for the excessive zero counts in the semiparametric framework we propose a generalized partially linear single index model for the mean of the poisson component the probability of zero or both we develop the estimation and inference procedure via a profile maximum likelihood method under some mild conditions we establish the asymptotic properties of the profile likelihood estimators the finite sample performance of the proposed method is demonstrated by simulation studies and the new model is illustrated with a medical care dataset

variable selection for partially linear models with measurement errors this article focuses on variable selection for partially linear models when the covariates are measured with additive errors we propose two classes of variable selection procedures penalized least squares and penalized quantile regression using the nonconvex penalized principle the first procedure corrects the bias in the loss function caused by the measurement error by applying the so called correction for attenuation approach whereas the second procedure corrects the bias by using orthogonal regression the sampling properties for the two procedures are investigated the rate of convergence and the asymptotic normality of the resulting estimates are established we further demonstrate that with proper choices of the penalty functions and the regularization parameter the resulting estimates perform asymptotically as well as an oracle procedure as proposed by fan and li choice of smoothing parameters is also discussed finite sample performance of the proposed variable selection procedures is asse

variance function partially linear single index models we consider heteroscedastic regression models where the mean function is a partially linear single index model and the variance function depends upon a generalized partially linear single index model we do not insist that the variance function depend only upon the mean function as happens in the classical generalized partially linear single index model we develop efficient and practical estimation methods for the variance function and for the mean function asymptotic theory for the parametric and nonparametric parts of the model is developed simulations illustrate the results an empirical example involving ozone levels is used to further illustrate the results and is shown to be a case where the variance function does not depend upon the mean function

measurement errors in quantile regression models abstract this paper develops estimation and inference for quantile regression models with measurement errors we propose an easily implementable semiparametric two step estimator when repeated measures for the covariates are available building on recent theory on z estimation with infinite dimensional parameters consistency and asymptotic normality of the proposed estimator are established we also develop statistical inference procedures and show the validity of a bootstrap approach to implement the methods in practice monte carlo simulations assess the finite sample performance of the proposed methods we apply the methods to the investment equation model using a firm level data with repeated measures of investment demand tobin s q we document strong heterogeneity in the sensitivity of investment to tobin s q and cash flow across the conditional distribution of investment the cash flow sensitivity is relatively larger at the lower part of the distribution providing evidence that these firms are more exposed to and dependent on fluctuations in internal finance

asymptotic variance of semiparametric estimators with generated regressors we study the asymptotic distribution of three step estimators of a finite dimensional parameter vector where the second step consists of one or more nonparametric regressions on a regressor that is estimated in the first step the first step estimator is either parametric or nonparametric using newey s 1994 path derivative method we derive the contribution of the first step estimator to the influence function in this derivation it is important to account for the dual role that the first step estimator plays in the second step nonparametric regression that is that of conditioning variable and that of argument

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

semiparametric analysis of complex polygenic gene environment interactions in case control studies many methods have recently been proposed for efficient analysis of case control studies of gene environment interactions using a retrospective likelihood framework that exploits the natural assumption of gene environment independence in the underlying population however for polygenic modelling of gene environment interactions which is a topic of increasing scientific interest applications of retrospective methods have been limited due to a requirement in the literature for parametric modelling of the distribution of the genetic factors we propose a general computationally simple semiparametric method for analysis of case control studies that allows exploitation of the assumption of gene environment independence without any further parametric modelling assumptions about the marginal distributions of any of the two sets of factors the method relies on the key observation that an underlying efficient profile likelihood depends on the distribution of genetic factors only through certain expectation terms that can be evaluated empirically we develop asymptotic inferential theory for the estimator and evaluate its numerical performance via simulation studies an application of the method is presented

semiparametric estimation of models with conditional moment restrictions in the presence of nonclassical measurement errors abstract this paper develops a framework for the analysis of semiparametric conditional moment models with endogenous and mismeasured causes which is of empirical importance we show that one set of valid instruments is sufficient to control for both endogeneity and measurement errors of the causes of interest which has been observed in linear parametric models two step consistent estimators of the parameters of interest are proposed we also show that the proposed estimators are consistent with a rate faster than n 1 4 under a certain metric and the proposed estimators of the finite dimensional unknown parameters obtain root n asymptotic normality monte carlo evidences show that the proposed estimators perform well under a variety of identification conditions an application to instrumental variables estimation of engel curves illustrates the usefulness of our method it supports that correcting for both endogeneity and measurement errors on total expenditure is substantial in estimating economically meaningful engel curves

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

identification of additive and polynomial models of mismeasured regressors without instruments abstract we show nonparametric point identification of a measurement error model with covariates that can be interpreted as invalid instruments our main contribution is to replace standard exclusion restrictions with the weaker assumption of additivity in the covariates measurement errors are ubiquitous and additive models are popular so our results combining the two should have widespread potential application we also identify a model that replaces the nonparametric function of the mismeasured regressor with a polynomial in that regressor and other covariates this allows for rich interactions between the variables at the expense of introducing a parametric restriction our identification proofs are constructive and so can be used to form estimators we establish root n asymptotic normality for one of our estimators

robust estimation with many instruments abstract linear instrumental variables models are widely used in empirical work but often associated with low estimator precision this paper proposes an estimator that is robust to outliers and shows that the estimator is minimax optimal in a class of estimators that includes the limited maximum likelihood estimator liml intuitively this optimal robust estimator combines liml with winsorization of the structural residuals and the winsorization leads to improved precision under thick tailed error distributions consistency and asymptotic normality of the estimator are established under many instruments asymptotics and a consistent variance estimator which allows for asymptotically valid inference is provided

semiparametric binary choice panel data models without strictly exogeneous regressors previous estimators of binary choice panel data models with fixed effects require strong parametric error asumptions strictly exogeneous regressors or both this is because nonlinearity of the model precludes the use of the moment conditions on differences based estimators that are generally employed for linear models without strictly exogeneous regressors based on the cross section binary choice estimator in lewbel 2000a we show how discrete choice panel data models with fixed effects can be estimated with only predetermined regressors the estimator is semiparametric in that the error distribution is not specified it allows for some general forms of heteroskedasticity and converges at rate root n this abstract was borrowed from another version of this item

efficient estimation and computation of parameters and nonparametric functions in generalized semi non parametric regression models abstract the efficiency of estimation for the parameters in semiparametric models has been widely studied in the literature bickel et al 1993 in this paper we study efficient estimators for both parameters and nonparametric functions in a class of generalized semi non parametric regression models which cover commonly used semiparametric models such as partially linear models partially linear single index models and two sample semiparametric models we propose a maximum likelihood principle combined with the local linear technique for estimating the parameters and nonparametric functions the proposed estimators of the parameters and a linear functional of the nonparametric functions are consistent and asymptotically normal and are further shown to be semiparametrically efficient an efficient computational algorithm to achieve the maximization is proposed extensive simulation experiments show the superiority of the proposed methods three real data examples are analyzed and presented as an illustration

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

nonparametric regression with nonparametrically generated covariates we analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable but have be estimated from data in a preliminary step these so called generated covariates appear in numerous applications including two stage nonparametric regression estimation of simultaneous equation models or censored regression models yet so far there seems to be no general theory for their impact on the final estimator s statistical properties our paper provides such results we derive a stochastic expansion that characterizes the influence of the generation step on the final estimator and use it to derive rates of consistency and asymptotic distributions accounting for the presence of generated covariates

asymptotics for semiparametric econometric models via stochastic equicontinuity this paper provides a general framework for proving the square root of t consistency and asymptotic normality of a wide variety of semiparametric estimators the class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator the method of proof exploits results concerning the stochastic equicontinuity of stochastic processes the results are applied to the problem of semiparametric weighted least squares estimation of partially parametric regression models primitive conditions are given for square root of t consistency and asymptotic normality of this estimator copyright 1994 by the econometric society

efficient semiparametric estimation for endogenously stratified regression via smoothed likelihood abstract this paper presents efficient semiparametric estimators for endogenously stratified regression with two strata in the case where the error distribution is unknown and the regressors are independent of the error term the method is based on the use of a kernel smoothed likelihood function which provides an explicit solution for the maximization problem for the unknown density function without losing information in the asymptotic limit we consider both standard stratified sampling and variable probability sampling and allow for the population shares of the strata to be either unknown or known a priori

nonparametric identification of discrete choice models with lagged dependent variables abstract variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity kasahara and shimotsu 2009 browning and carro 2014 in some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates this paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates the identification argument is related to that of honore and lewbel 2002 in that it requires a special regressor lewbel 1998 but it does not assume an additively separable latent index identification requires only 3 time periods neither stationarity nor time homogeneity is imposed and the distribution of the initial condition is not restricted apart from conditions required for the special regressor i demonstrate the result through a monte carlo simulation

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

identification and estimation of nonlinear models with misclassification error using instrumental variables a general solution abstract this paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables the misclassification error is allowed to be correlated with all the explanatory variables in the model it is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns such a claim requires solving a complicated nonlinear system of equations this paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system the solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions therefore the latent model is nonparametrically identifiable and directly estimable using instrumental variables the results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities an alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting the nonparametric identification in this paper directly leads to a n consistent semiparametric estimator the monte carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

estimating panel data models in the presence of endogeneity and selection we consider estimation of panel data models with sample selection when the equation of interest contains endogenous explanatory variables as well as unobserved heterogeneity assuming that appropriate instruments are available we propose several tests for selection bias and two estimation procedures that correct for selection in the presence of endogenous regressors the tests are based on the fixed effects two stage least squares estimator thereby permitting arbitrary correlation between unobserved heterogeneity and explanatory variables the first correction procedure is parametric and is valid under the assumption that the errors in the selection equation are normally distributed the second procedure estimates the model parameters semiparametrically using series estimators in the proposed testing and correction procedures the error terms may be heterogeneously distributed and serially dependent in both selection and primary equations because these methods allow for a rather flexible structure of the error variance and do not impose any nonstandard assumptions on the conditional distributions of explanatory variables they provide a useful alternative to the existing approaches presented in the literature

formulations of support vector machines a note from an optimization point of view in this article we discuss issues about formulations of support vector machines svm from an optimization point of view first svms map training data into a higher maybe infinite dimensional space currently primal and dual formulations of svm are derived in the finite dimensional space and readily extend to the infinite dimensional space we rigorously discuss the primal dual relation in the infinite dimensional spaces second svm formulations contain penalty terms which are different from unconstrained penalty functions in optimization traditionally unconstrained penalty functions approximate a constrained problem as the penalty parameter increases we are interested in similar properties for svm formulations for two of the most popular svm formulations we show that one enjoys properties of exact penalty functions but the other is only like traditional penalty functions which converge when the penalty parameter goes to infinity