semi nonparametric estimation of binary response models with an application to natural resource valuation abstract a semi nonparametric binary response model is estimated to obtain the willingness to pay for the environmental quality improvement when the willingness to pay is restricted to be nonnegative the model estimation is straightforward by using conventional maximum likelihood software because the semi nonparametric model is the generalization of the parametric model the generality can be assessed by a likelihood ratio test by using an existing referendum survey data set it is shown that the semi nonparametric estimation provides a significant improvement over the parametric estimation the willingness to pay is sensitive to the distribution assumption

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

nonparametric least squares estimation of a multivariate convex regression function this paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional we characterize and discuss the computation of such an estimator via the solution of certain quadratic and linear programs mild sufficient conditions for the consistency of this estimator and its subdifferentials in fixed and stochastic design regression settings are provided we also consider a regression function which is known to be convex and componentwise nonincreasing and discuss the characterization computation and consistency of its least squares estimator

non parametric hypothesis testing procedures and applications to demand analysis abstract this paper proposes a test of the hypothesis that a possibly vector valued regression function g lies in a particular compact family of functions f where f is not necessarily a finite dimensional parametric family under the assumption of a known covariance matrix of the errors the test is shown to be consistent for a broad range of alternatives and an upper bound on the significance level is established it is shown how the test may be used to test the utility maximization hypothesis and homotheticity and the paper indicates how to apply the test to a broad range of other non parametric hypotheses

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

asymptotic efficiency in semi parametric models with censoring abstract we consider a regression model subject to bivariate censoring in which the errors are independent of the explanatory variables our objective is to drop the assumption of bivaraite normality and obtain an information bound on asymptotic efficiency when the error distribution is unrestricted except for smoothness and regularity conditions this bound has simple form if there are no exclusion restrictions on the selection equation then positive information requires a restriction on the regression slope parameters and a continuous distribution for a component of the explanatory variables we also consider a binary choice model under the weak assumption that the error distribution has zero median conditional on the explanatory variables here the semi parametric information bound is zero hence although a consistent estimator exists it is not possible to attain covergence at rate 1 n

nonparametric identification and estimation of polychotomous choice models abstract in this paper we provide conditions guaranteeing the identification of nonparametric polychotomous choice models in these models neither the subutility function of observable attributes nor the distribution of the unobservable random terms is specified parametrically sets of nonparametric functions that possess properties that are often implied by economic theory and satisfy the restrictions required to identify the models are described we use the identification results to develop nonparametric strongly consistent estimators for the subutility function of observable attributes the results concern models in which the distribution of the unobservable random terms both depend and do not depend on the observable characteristics

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

minimal length elements in twisted conjugacy classes of finite coxeter groups let w be a finite coxeter group and let f be an automorphism of w that leaves the set of generators of w invariant we establish certain properties of elements of minimal length in the f conjugacy classes of w that allow us to define character tables for the corresponding twisted iwahori hecke algebras these results are extensions of results obtained by geck and pfeiffer in the case where f is trivial

generalized additive and index models with shape constraints summary we study generalized additive models with shape restrictions e g monotonicity convexity and concavity imposed on each component of the additive prediction function we show that this framework facilitates a non parametric estimator of each additive component obtained by maximizing the likelihood the procedure is free of tuning parameters and under mild conditions is proved to be uniformly consistent on compact intervals more generally our methodology can be applied to generalized additive index models here again the procedure can be justified on theoretical grounds and like the original algorithm has highly competitive finite sample performance practical utility is illustrated through the use of these methods in the analysis of two real data sets our algorithms are publicly available in the r package scar short for shape constrained additive regression

bootstrap critical values for tests based on the smoothed maximum score estimator the smoothed maximum score estimator of the coefficient vector of a binary response model is consistent and asymptotically normal under weak distributional assumptions however the differences between the true and nominal levels of tests based on smoothed maximum score estimates can be very large in finite samples when first order asymptotics are used to obtain critical values this paper gives conditions under which the differences between the true and nominal levels can be reduced by using the bootstrap to obtain critical values a set of monte carlo experiments illustrates the numerical performance of the bootstrap

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

on theoretical and empirical aspects of marginal distribution choice models in this paper we study the properties of a recently proposed class of semiparametric discrete choice models referred to as the marginal distribution model mdm by optimizing over a family of joint error distributions with prescribed marginal distributions surprisingly the choice probabilities arising from the family of generalized extreme value models of which the multinomial logit model is a special case can be obtained from this approach despite the difference in assumptions on the underlying probability distributions we use this connection to develop flexible and general choice models to incorporate consumer and product level heterogeneity in both partworths and scale parameters in the choice model furthermore the extremal distributions obtained from the mdm can be used to approximate the fisher s information matrix to obtain reliable standard error estimates of the partworth parameters without having to bootstrap the method we use simulated and empirical data sets to test the performance of this approach we evaluate the performance against the classical multinomial logit mixed logit and a machine learning approach that accounts for partworth heterogeneity our numerical results indicate that mdm provides a practical semiparametric alternative to choice modeling this paper was accepted by eric bradlow special issue on business analytics

origins of the limited information maximum likelihood and two stage least squares estimators theil basmann and sargan are often credited with the development of the two stage least squares tsls estimator of the coefficients of one structural equation in a simultaneous equations model however anderson and rubin had earlier derived the asymptotic distribution of the limited information maximum likelihood liml estimator by finding the asymptotic distribution of what is essentially the tsls estimator

discrete factor approximations in simultaneous equation models estimating the impact of a dummy endogenous variable on a continuous outcome this paper contains a monte carlo evaluation of estimators used to control for endogeneity of dummy explanatory variables in continuous outcome regression models when the true model has bivariate normal disturbances estimators using discrete factor approximations compare favorably to efficient estimators in terms of precision and bias these approximation estimators dominate all the other estimators examined when the disturbances are non normal the experiments also indicate that one should liberally add points of support to the discrete factor distribution the paper concludes with an application of the discrete factor approximation to the estimation of the impact of marriage on wages

estimating a generalized correlation coefficient for a generalized bivariate probit model abstract in this paper we consider semiparametric estimation of a generalized correlation coefficient in a generalized bivariate probit model the generalized correlation coefficient provides a simple summary statistic measuring the relationship between the two binary decision processes in a general framework our semiparametric estimation procedure consists of two steps combining semiparametric estimators for univariate binary choice models with the method of maximum likelihood for the bivariate probit model with nonparametrically generated regressors the estimator is shown to be consistent and asymptotically normal the estimator performs well in our simulation study

rank estimation of a location parameter in the binary choice model abstract this paper proposes a rank based estimator for a location parameter in the binary choice model under a monotonic index and symmetry condition given an initial n consistent estimator for the slope parameter the estimator converges at the usual parametric rate compared with existing estimators no nonparametric smoothing is needed here a small monte carlo study illustrates the usefulness of the estimator we also point out that the location and slope parameters can be jointly estimated

nonparametric and distribution free estimation of the binary threshold crossing and the binary choice models in this paper it is shown that it is possible to identify binary threshold crossing models and binary choice models without imposing any parametric structure either on the systematic function of observable exogenous variables or on the distribution of the random term this identification result is employed to develop a fully nonparametric maximum likelihood estimator for both the function of observable exogenous variables and the distribution of the random term the estimator is shown to be strongly consistent and a two step procedure for its calculation is developed the paper also includes examples of economic models that satisfy the conditions that are necessary to apply the results

a nonparametric multiple choice method within the random utility framework abstract many researchers use categorical data analysis to recover individual consumption preferences but the standard discrete choice models require restrictive assumptions to improve the flexibility of discrete choice data analysis we propose a nonparametric multiple choice model that applies the penalized likelihood method within the random utility framework we show that the deterministic component of the random utility function in the model is a cubic smoothing spline function the method subsumes the conventional conditional logit model mcfadden 1973 in zarembka p ed frontiers in econometrics as a special case in this paper we present the model describe the estimator provide the computational algorithm of the model and demonstrate the model by applying it to nonmarket valuation of recreation sites

distribution free maximum likelihood estimator of the binary choice model1 is a given function of the exogenous variables z and unknown parameters 9 representing the systematic component of the utility difference and f is the distribution function of the random component of the utility difference this paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function f and proves that this estimator is consistent f is also consistently estimated the method uses maximum likelihood estimation in which the likelihood is maximized not only over the parameter 9 but also over a space which contains all distribution functions

duration dependence and nonparametric heterogeneity a monte carlo study we examine the behaviour of the nonparametric maximum likelihood estimator npmle for a discrete duration model with unobserved heterogeneity and unknown duration dependence we find that a nonparametric specification of either the duration dependence or unobserved heterogeneity when the other feature of the hazard is known to be absent leads to estimators that are well behaved even in modestly sized samples in contrast there is a large and systematic bias in the parameters of these components when both are specified nonparametrically as well as a complementary bias in the coefficients on observed heterogeneity furthermore these biases diminish very gradually as sample size increases we find that a minor modification of the quasilikelihood that penalizes specifications with many points of support leads to a dramatic improvement

maximum score estimation of disequilibrium models and the role of anticipatory price setting abstract in this paper a general model of disequilibrium quantity determination under median regression assumptions is combined with weak assumptions on the price adjustment to yield a consistent maximum score estimator in contrast to sapra 1986 the supply and demand parameters are separately identifiable and the estimator employs all of the observed data the price adjustment assumptions can be motivated by the anticipatory pricing model of green and laffont 1981 in contrast to the green laffont model however our assumptions only require that long run walrasian prices have positive probability as an illustrative application maximum score estimates of a model of the us commercial loan market are computed and compared to maximum likelihood estimates monte carlo results are also reported

identification and estimation in a correlated random coefficients binary response model we study a linear index binary response model with random coefficients bb allowed to be correlated with regressors x we identify the mean of the distribution of b and show how the mean can be interpreted as a vector of expected relative effects we use instruments and a control vector v to make x independent of b given v this leads to a localize then average approach to both identification and estimation we develop a n consistent and asymptotically normal estimator of a trimmed mean of the distribution of bb explore its small sample performance through simulations and present an application

reduced rank regression for blocks of simultaneous equations abstract reduced rank regression analysis provides maximum likelihood estimators of a matrix of regression coefficients of specified rank and of corresponding linear restrictions on such matrices these estimators depend on the eigenvectors of an effect matrix in the metric of an error covariance matrix in this paper it is shown that the maximum likelihood estimator of the restrictions can be approximated by a function of the effect matrix alone the procedures are applied to a block of simultaneous equations the block may be over identified in the entire model and the individual equations just identified within the block the procedures are generalizations of the limited information maximum likelihood and two stage least squares estimators

semiparametric identification and heterogeneity in discrete choice dynamic programming models abstract empirical discrete choice dynamic programming models have become important empirical tools a question that arises in estimation and interpretation of the results from these specifications is which combination of data and assumptions are needed to overcome problems of heterogeneity selection and omited variables bias this paper addresses this question by considering nonparametric identification of a version of the model that allows for quite general forms of unobservable and information structures i show that the model can be identified under conditions similar to a static polychotomous choice model using a stochastic version of an identification of infinity argument utility can be identified up to a monotonic transformation of the observables under strong support conditions and two types of exclusion restriction the first type is similar to a standard static exclusion restriction a variable that influences the first period decision but does not enter the second period decision directly the second type requires a variable that does not affect the utility of the first option directly but is known during the first period and has predictive power on the choice during the second i also provide two specifications under which the full error structure can be identified this requires the additional assumption of stochastic innovations in the observables i then use the model to estimate schooling decisions in which students deciding whether to drop out of high school account for the option value of attending college

identification of binary response models abstract this article studies identification of the threshold crossing model of binary response most research on binary response has considered specific estimators and tests the study of identification exposes the foundations of binary response analysis by making explicit the assumptions needed to justify different methods it also clarifies the connections between reduced form and structural analyses of binary response data assume that the binary outcome z is determined by an observable random vector x and by an unobservable scalar u through a model z 1 x u 0 also assume that fu x the probability distribution of u conditional on x is continuous and strictly increasing given these maintained assumptions we investigate the identifiability of given the following restrictions on the distributions fu x x x mean independence quantile independence index sufficiency statistical independence and statistical independence with the distribution known we find that mean independence has n

contragredient representations and characterizing the local langlands correspondence we consider the question what is the contragredient in terms of l homomorphisms we conjecture that it corresponds to the chevalley automorphism of the l group and prove this in the case of real groups the proof uses a characterization of the local langlands correspondence over r we also consider the related notion of hermitian dual in the case of gl n bbb r

on the bias in flexible functional forms and an essentially unbiased form the fourier flexible form abstract the fourier flexible form and its derived expenditure system are introduced subject to smoothness conditions on the consumer s true indirect utility function the consumer s true expenditure system must be of the fourier form over the region of interest in an empirical investigation arbitrarily accurate finite parameter approximations of the consumer s true expenditure system are obtained by dropping all high order terms of the fourier expenditure system past an appropriate truncation point the resulting finite parametersystem is tractable in empirical studies the reader who is primarily interested in applications need only read the second and fifth sections the remainder of the article is concerned with the verification of these claims and an investigation of some aspects of the bias in translog specifications

estimation of the binary response model using a mixture of distributions estimator mod abstract in this paper we develop a semiparametric sieve estimator which is termed a mixture of distributions estimator mod to estimate a binary response model when the distribution of the errors is unknown the estimator of the distribution function is composed of a mixture of smooth distributions where the number of mixtures increases with the sample size the model is semiparametric because it is assumed that a parametric index type restriction holds optimal rates of convergence are established for the distribution function under the l 2 norm and conditions are derived under which estimates of the parametric component are asymptotically normal an appealing feature about mod is that it is possible to restrict the estimator of the distribution function a priori to be smooth nonnegative nondecreasing and to integrate to one this has important practical and theoretical implications

nonparametric two stage estimation of conditional choice probabilities in a binary choice model under uncertainty abstract in this paper estimation of conditional choice probabilities in a binary choice model under uncertainty is considered under weak nonparametric restrictions on expectations and the error distribution the estimation method follows a two stage strategy the first stage estimates expectations using realizations of agents future and the second stage estimates conditional choice probabilities using choice data and the expectations estimates this paper gives conditions under which the two stage nonparametric kernel estimator is uniformly strongly consistent and asymptotically normal

unbiased determination of production technologies abstract to determine whether an industry exhibits constant returns to scale whether the production function is homothetic or whether inputs are separable a common approach is to specify a cost function estimate its parameters using data such as prices and quantities of inputs and then test the parametric restrictions corresponding to constant returns a homothetic technology or separability statistically such inferences are valid if the true cost function is a member of the parametric class considered otherwise the inference is biased that is the true rejection probability is not necessarily adequately approximated by the nominal size of the statistical test the use of fixed parameter flexible functional forms such as the translog the generalized leontief or the box cox will not alleviate this problem the fourier flexible form differs fundamentally from other flexible forms in that it has a variable number of parameters and a known bound depending on the number of parameters on the error as measured by the sobolev norm of approximation to an arbitrary cost function thus it is possible to construct statistical tests for constant returns a homothetic technology or separability which are asymptotically size by letting the number of parameters of the fourier flexible form depend on sample size that is the true rejection probability converges to the nominal size of the test as sample size tends to infinity the rate of convergence depends on the smoothness of the true cost function the more times is differentiable the true cost function the faster the convergence the method is illustrated using the data on aggregate u s manufacturing of berndt and wood 1975 1979 and berndt and khaled 1979

panel binary variables and sufficiency generalizing conditional logit this paper extends the conditional logit approach rasch andersen chamberlain used in panel data models of binary variables with correlated fixed effects and strictly exogenous regressors in a two period two state model necessary and sufficient conditions on the joint distribution function of the individual and period specific shocks are given such that the sum of individual binary variables across time is a sufficient statistic for the individual effect by extending a result of chamberlain it is shown that root n consistent regular estimators can be constructed in panel binary models if and only if the property of sufficiency holds in applied work the estimation method amounts to quasi differencing the binary variables as if they were continuous variables and transforming a panel data model into a cross section model semiparametric approaches can then be readily applied

consistent estimation of limited dependent variable models despite misspecification of distribution abstract by exploiting conditions on the behavior of regressors estimators are developed which are consistent up to a factor of proportionality for the slope coefficients of the regression function of a imperfectly observed dependent variable limited dependent variables are a special case of interest the consistency is robust to misspecification of the distribution of the latent dependent variable the estimators are weighted pseudo maximum likelihood estimators which can be readily computed using popular methods and software

semiparametric estimation of monotone and concace utility functions for polychotomous choice models this paper introduces a semiparametric estimation method for polychotomous choice models the method does not require a parametric structure for the systematic subutility of observable exogenous variables the distribution of the random terms is assumed to be known up to a finite dimensional parameter vector in contrast previous semiparametric methods of estimating discrete choice models have concentrated on relaxing parametric subutility parametrically specified the systematic subutility is assumed to possess properties such as monotonicity and concavity that are typically assumed in microeconomic theory the estimator for the systematic subutility and the parameter vector of the distribution is shown to be strongly consistent a computational technique to calculate the estimators is developed copyright 1991 by the econometric society

nonparametric option pricing under shape restrictions frequently economic theory places shape restrictions on functional relationships between economic variables this paper develops a method to constrain the values of the first and second derivatives of nonparametric locally polynomial estimators we apply this technique to estimate the state price density spd or risk neutral density implicit in the market prices of options the option pricing function must be monotonic and convex simulations demonstrate that nonparametric estimates can be quite feasible in the small samples relevant for day to day option pricing once appropriate theory motivated shape restrictions are imposed using s p 500 option prices we show that unconstrained nonparametric estimators violate the constraints during more than half the trading days in 1999 unlike the constrained estimator we propose

adaptive estimation in time series regression models this work develops adaptive estimators for a linear regression model with serially correlated errors we show that these results continue to hold when the order of the arma process characterizing the errors is unknown the finite sample results are promising indicating that substantial efficiency gains may be possible for samples as small as 50 observations we use these estimators to investigate the behavior of the forward foreign exchange market

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

bayesian inference for semiparametric binary regression abstract we propose a regression model for binary response data that places no structural restrictions on the link function except monotonicity and known location and scale predictors enter linearly we demonstrate bayesian inference calculations in this model by modifying the dirichlet process we obtain a natural prior measure over this semiparametric model and we use polya sequence theory to formulate this measure in terms of a finite number of unobserved variables we design a markov chain monte carlo algorithm for posterior simulation and apply the methodology to data on radiotherapy treatments for cancer

distribution free estimation of the random coefficient dummy endogenous variable model this paper considers the estimation of the random coefficient dummy endogenous variable model under a symmetry and index condition for the error distribution we follow a two step approach the selection equation is estimated first in the second step an instrumental variables estimator is proposed for the ourcome equation through a pairwise comparison method our approach can be readily extended to the general switching regression model in constrast to the existing literature on sample selection models the exclusion restriction is not needed here for model identification furthermore the intercept term for the outcome equation can be estimated at the usual parametric rate

nonparametric estimation of homothetic and homothetically separable functions for vectors x and w let r x w be a function that can be nonparametrically estimated consistently and asymptotically normally we provide consistent asymptotically normal estimators for the functions g and h where r x w h g x w g is linearly homogeneous and h is monotonic in g this framework encompasses homothetic and homothetically separable functions such models reduce the curse of dimensionality provide a natural generalization of linear index models and are widely used in utility production and cost function applications extensions to related functional forms include a generalized partly linear model with unknown link function we provide simulation evidence on the small sample performance of our estimator and we apply our method to a chinese production dataset

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

distribution free estimation of heteroskedastic binary response models using probit logit criterion functions abstract in this paper estimators for distribution free heteroskedastic binary response models are proposed the estimation procedures are based on relationships between distribution free models with a conditional median restriction and parametric models such as probit logit exhibiting multiplicative heteroskedasticity the first proposed estimator is based on the observational equivalence between the two models and is a semiparametric sieve estimator see e g gallant and nychka 1987 ai and chen 2003 and chen et al 2005 for the regression coefficients based on maximizing standard logit probit criterion functions such as nlls and mle this procedure has the advantage that choice probabilities and regression coefficients are estimated simultaneously the second proposed procedure is based on the equivalence between existing semiparametric estimators for the conditional median model manski 1975 manski 1985 horowitz 1992 and the standard parametric probit logit nlls estimator this estimator has the advantage of being implementable with standard software packages such as stata distribution theory is developed for both estimators and a monte carlo study indicates they both perform well in finite samples

minimal length elements in some double cosets of coxeter groups abstract we study the minimal length elements in some double cosets of coxeter groups and use them to study lusztig s g stable pieces and the generalization of g stable pieces introduced by lu and yakimov we also use them to study the minimal length elements in a conjugacy class of a finite coxeter group and prove a conjecture in m geck s kim g pfeiffer minimal length elements in twisted conjugacy classes of finite coxeter groups j algebra 229 2 2000 570 600

semiparametric analysis of discrete response asymptotic properties of the maximum score estimator abstract this paper is concerned with the estimation of the model med y x x from a random sample of observations on sgn y x manski 1975 introduced the maximum score estimator of the normalized parameter vector in the present paper strong consistency is proved it is also proved that the maximum score estimate lies outside any fixed neighborhood of with probability that goes to zero at exponential rate

estimating features of a distribution from binomial data we propose estimators of previous termfeatures of the distributionnext term of an unobserved random variable w what is observed is previous termanext term sample of y v x where previous termanext term binary y equals one when w exceeds previous termanext term threshold v determined by experimental design and x are covariates potential applications include bioassay and destructive duration analysis our empirical application is referendum contingent valuation in resource economics where one is interested in previous termfeatures of the distributionnext term of values w willingness to pay placed by consumers on previous termanext term public good such as endangered species sample consumers with characteristics x are asked whether they favor with y 1 if yes and zero otherwise previous termanext term referendum that would provide the good at previous termanext term cost v specified by experimental design this paper provides estimators for quantiles and conditional on x moments of w under both nonparametric and semiparametric specifications

estimation of best predictors of binary response abstract this paper investigates analog estimation of predictors of binary response given semiparametric restrictions on the response process results are presented for the isotonic response model and for the weaker single crossing model the isotonic model assumes that the response probability is monotone in a linear function of the conditioning variables in the single crossing model the response probability is above a given value when a linear function of the conditioning variables is positive and below that value otherwise it is found that analog estimators computed under the isotonicity restriction are generally consistent estimation under the single crossing restriction is consistent only for special loss functions

nonparametric maximum likelihood methods for binary response models with random coefficients the venerable method of maximum likelihood has found numerous recent applications in nonparametric estimation of regression and shape constrained densities for mixture models the nonparametric max

nonparametric matching and efficient estimators of homothetically separable functions for vectors z and w and scalar v let r v z w be a function that can be non parametrically estimated consistently and asymptotically normally such as a distribution density or conditional mean regression function we provide consistent asymptotically normal nonparametric estimators for the functions g and h where r v z w h vg z w and some related models this framework encompasses homothetic and homothetically separable functions and transformed partly additive models r v z w h v g z w for unknown functions g and h such models reduce the curse of dimensionality provide a natural generalization of linear index models and are widely used in utility production and cost function applications we also provide an estimator of g that is oracle efficient achieving the same performance as an estimator based on local least squares when h is known

dummy endogenous variables in weakly separable models in this paper we consider the nonparametric identification and estimation of the average effect of a dummy endogenous regressor in models where the regressors are weakly but not additively separable from the error term the model is not required to be strictly increasing in the error term and the class of models considered includes limited dependent variable models such as discrete choice models conditions are established conditions under which it is possible to identify the average effect of the dummy endogenous regressor in a weakly separable model without relying on parametric functional form or distributional assumptions and without the use of large support conditions

semiparametric least squares sls and weighted sls estimation of single index models abstract for the class of single index models i construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 n consistency and asymptotic normality this class of models includes censored and truncated tobit models binary choice models and duration models with unobserved individual heterogeneity and random censoring i also investigate a weighting scheme that achieves the semiparametric efficiency bound

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

uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing a new uniform expansion is introduced for sums of weighted kernel based regression residuals from nonparametric or semiparametric models this result is useful for deriving asymptotic properties of semiparametric estimators and test statistics with data dependent bandwidth random trimming and estimated weights an extension allows for generated regressors without requiring the calculation of functional derivatives example applications are provided for a binary choice model with selection including a new semiparametric maximum likelihood estimator and a new directional test for correct specification of the average structural function a supplement contains general results on uniform rates for kernel estimators additional applications and primitive sufficient conditions for high level assumptions

distribution free and link free estimation for the sample selection model abstract the prevalent estimation methods for the sample selection model rely heavily on parametric assumptions and are sensitive to departures from the underlying parametric assumptions see e g goldberger 1983 we propose an alternative estimation method the corrected maximum likelihood estimate which is consistent for the slope vector in the outcome equation up to a multiplicative scalar even through the parametric model on which the estimate is based might be misspecified as an important corollary it follows from our result that olsen s 1980 corrected ordinary least squares estimate is consistent if the outcome equation is linear without requiring olsen s assumptions on the joint error distribution

semiparametric maximum likelihood estimation of polychotomous and sequential choice models abstract this article considers semiparametric estimation of discrete choice models the estimation method is a semiparametric maximum likelihood method which generalizes klein and spady 1993 to the estimation of polychotomous choice and sequential choice models special emphasis is on the estimation of models with indices of which the density function is not bounded away from zero issues on trimming indices the correction of asymptotic bias and issues of negative kernel density estimation a semiparametric efficiency bound is derived for the polychotomous choice model with index restrictions our estimator is shown to be n consistent asymptotically normal and almost asymptotically efficient monte carlo experiments are provided to evaluate the finite sample performance of the estimator

lifting of elements of weyl groups abstract suppose g is a reductive algebraic group t is a cartan subgroup of g n norm t and w n t is the weyl group if w w has order d it is natural to ask about the orders lifts of w to n it is straightforward to see that the minimal order of a lift of w has order d or 2d but it can be a subtle question which holds we first consider the question of when w itself lifts to a subgroup of n in which case every element of w lifts to an element of n of the same order we then consider two natural classes of elements regular and elliptic in the latter case all lifts of w are conjugate and therefore have the same order we also consider the twisted case

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

a consistent bootstrap procedure for the maximum score estimator abstract in this paper we propose a new model based smoothed bootstrap procedure for making inference on the maximum score estimator of manski 1975 1985 and prove its consistency we provide a set of sufficient conditions for the consistency of any bootstrap procedure in this problem we compare the finite sample performance of different bootstrap procedures through simulation studies the results indicate that our proposed smoothed bootstrap outperforms other bootstrap schemes including the m out of n bootstrap additionally we prove a convergence theorem for triangular arrays of random variables arising from binary choice models which may be of independent interest

methods for estimating a conditional distribution function abstract motivated by the problem of setting prediction intervals in time series analysis we suggest two new methods for conditional distribution estimation the first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation it produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1 the second method involves an adjusted form of the nadaraya watson estimator it preserves the bias and variance properties of a class of second order estimators introduced by yu and jones but has the added advantage of always being a distribution itself our methods also have application outside the time series setting for example to quantile estimation for independent data this problem motivated the work of yu and jones

efficiency bounds for distribution free estimators of the binary choice and the censored regression models we derive lower bounds on the asymptotic variances for regular distribution free estimators of the parameters of the binary choice model and the censored regression tobit model a distribution free or semiparametric estimator is one that does not require any assumption about the distribution of the stochastic error term in the model apart from regularity conditions for the binary choice model we obtain an explicit lower bound for the asymptotic variance for the slope parameters or more generally the parameters of a nonlinear regression function in the underlying latent variable model but we find that there is no regular semiparametric estimator of the constant term identified by requiring the error distribution to have zero median lower bounds are also obtained under the further assumption that the error distribution is symmetric and in this case there is a finite lower bound for the constant term too comparison of the bounds with those for the classical parametric problem shows the loss of information due to lack of a priori knowledge of the functional form of the error distribution we give the conditions for equality of the parametric and semiparametric lower bounds in which case adaptive estimation may be possible both with and without the assumption of a symmetric error distribution in general adaptive estimation is not possible but one special case where these conditions hold is when the regression function is linear and the explanatory variables have a multivariate normal distribution the tobit model considered here is the censored nonlinear regression model with a fixed censoring point we again give an explicit lower bound for the asymptotic variance for the regression parameters this time including a constant term if the error term has zero median comparison with the corresponding lower bound for the parametric case shows that adaptive estimation is in general not possible for this model

on independence conditions in nonseparable models observable and unobservable instruments this paper develops identification results employing independence conditions among unobservable variables the independence conditions are used to derive first stage nonseparable reduced form functions once constructed these reduced form functions are employed to express the derivatives of nonseparable structural functions in terms of the derivatives of the reduced form functions for models with simultaneity we obtain the new results by combining the independence assumptions together with parametric specifications and exclusion restrictions for models with triangularity we allow all functions to be nonparametric and nonseparable in unobservable random terms for the latter we provide several equivalence results and discuss some of the trade offs between observable and unobservable instruments

identification in nonparametric limited dependent variable models with simultaneity and unobserved heterogeneity we extend the identification results for nonparametric simultaneous equations models in matzkin 2008 to situations where the observations on the vector of dependent variables might be limited and where the number of exogenous unobservable variables is larger than the number of dependent variables