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

the bivariate probit model maximum likelihood estimation pseudo true parameters and partial identification abstract this paper examines the notion of identification by functional form for two equation triangular systems for binary endogenous variables by providing a bridge between the literature on the recursive bivariate probit model and that on partial identification we evaluate the impact of functional form on the performance of quasi maximum likelihood estimators and investigate the practical importance of available instruments in both cases of correct and incorrect distributional specification finally we calculate average treatment effect bounds and demonstrate how properties of the estimators are explicable via a link between the notion of pseudo true parameters and the concepts of partial identification

estimation of cross sectional and panel data censored regression models with endogeneity it is very difficult to deal with endogeneity in limited dependent variables models unless strong assumptions are made on the exact relationship between the endogenous regressors and the instruments it is generally not possible to apply instrumental variable type techniques this paper derives moment conditions that are useful in estimating censored regression models with endogenous regressors these moment conditions are motivated by panel data censored regression models with predetermined but not strictly exogenous explanatory variables but the main insight is also applicable to cross sectional models with endogenous explanatory variables

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

n uniformly consistent density estimation in nonparametric regression models abstract the paper introduces a n consistent estimator of the probability density function of the response variable in a nonparametric regression model the proposed estimator is shown to have a uniform asymptotic normal distribution and it is computationally very simple to calculate a monte carlo experiment confirms our theoretical results the results derived in the paper adapt general u processes theory to the inclusion of infinite dimensional nuisance parameters

predictive updating methods with application to bayesian classification we propose algorithms based on random draws from predictive distributions of unknown quantities missing values for instance this procedure can either be iterative which is a special variation of the gibbs sampler or be sequential which is a variation of sequential imputation in the latter case one can update the posterior distribution with new observations easily the methods proposed have intuitive statistical implications and can be generalized to accommodate other bayesian like procedures we display some applications of the method in connection with the bayesian bootstrap classification hierarchical models and selection of variables in particular as an application of the method we present a unified treatment of switching regression models driven by a general binary process and we develop a bayesian testing procedure some simulations and a real example are used to illustrate the methods proposed

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

estimating functions of probability distributions from a finite set of samples this paper addresses the problem of estimating a function of a probability distribution from a finite set of samples of that distribution a bayesian analysis of this problem is presented the optimal properties of the bayes estimators are discussed and as an example of the formalism closed form expressions for the bayes estimators for the moments of the shannon entropy function are derived then numerical results are presented that compare the bayes estimator to the frequency counts estimator for the shannon entropy we also present the closed form estimators all derived elsewhere for the mutual information mathrm ensuremath chi 2 covariance and some other statistics c 1995 the american physical society

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

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

maximum likelihood estimation of a multi dimensional log concave density fn is shown to have smaller mean integrated squared error compared with kernel based methods even when we allow the use of a theoret ical optimal fixed bandwidth for the kernel estimator that would not be available in practice we also present a real data clustering example which shows that our methodology can be used in conjunction with the expectation maximization algorithm to fit finite mixtures of log concave densities

a two step semiparametric method to accommodate sampling weights in multiple imputation multiple imputation mi is a well established method to handle item nonresponse in sample surveys survey data obtained from complex sampling designs often involve features that include unequal probability of selection mi requires imputation to be congenial that is for the imputations to come from a bayesian predictive distribution and for the observed and complete data estimator to equal the posterior mean given the observed or complete data and similarly for the observed and complete variance estimator to equal the posterior variance given the observed or complete data more colloquially the analyst and imputer make similar modeling assumptions yet multiply imputed data sets from complex sample designs with unequal sampling weights are typically imputed under simple random sampling assumptions and then analyzed using methods that account for the sampling weights this is a setting in which the analyst assumes more than the imputer which can led to biased estimates and anti conservative inference less commonly used alternatives such as including case weights as predictors in the imputation model typically require interaction terms for more complex estimators such as regression coefficients and can be vulnerable to model misspecification and difficult to implement we develop a simple two step mi framework that accounts for sampling weights using a weighted finite population bayesian bootstrap method to validly impute the whole population including item nonresponse from the observed data in the second step having generated posterior predictive distributions of the entire population we use standard iid imputation to handle the item nonresponse simulation results show that the proposed method has good frequentist properties and is robust to model misspecification compared to alternative approaches we apply the proposed method to accommodate missing data in the behavioral risk factor surveillance system when estimating means and parameters of regression models

semiparametric and nonparametric estimation of sample selection models under symmetry this paper considers the semiparametric estimation of binary choice sample selection models under a joint symmetry assumption our approaches overcome various drawbacks associated with existing estimators in particular our method provides root n consistent estimators for both the intercept and slope parameters of the outcome equation in a heteroscedastic framework without the usual cross equation exclusion restriction or parametric specification for the error distribution and or the form of heteroscedasticity our two step estimators are shown to be consistent and asymptotically normal a monte carlo simulation study indicates the usefulness of our approaches

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

a smoothed maximum score estimator for the binary response model this paper describes a semiparametric estimator for binary response models in which there may be arbitrary heteroskedasticity of unknown form the estimator is obtained by maximizing a smoothed version of the objective function of c manski s maximum score estimator the smoothing procedure is similar to that used in kernel nonparametric density estimation the resulting estimator s rate of convergence in probability is the fastest possible under the assumptions that are made the centered normalized estimator is asymptotically normally distributed methods are given for consistently estimating the parameters of the limiting distribution and for selecting the bandwidth required by the smoothing procedure copyright 1992 by the econometric society

generalized bootstrap for estimating equations we introduce a generalized bootstrap technique for estimators obtained by solving estimating equations some special cases of this generalized bootstrap are the classical bootstrap of efron the delete d jackknife and variations of the bayesian bootstrap the use of the proposed technique is discussed in some examples distributional consistency of the method is established and an asymptotic representation of the resampling variance estimator is obtained

inference on endogenously censored regression models using conditional moment inequalities under a quantile restriction randomly censored regression models can be written in terms of conditional moment inequalities we study the identified features of these moment inequalities with respect to the regression parameters where we allow for covariate dependent censoring endogenous censoring and endogenous regressors these inequalities restrict the parameters to a set we show regular point identification can be achieved under a set of interpretable sufficient conditions we then provide a simple way to convert conditional moment inequalities into unconditional ones while preserving the informational content our method obviates the need for nonparametric estimation which would require the selection of smoothing parameters and trimming procedures without the point identification conditions our objective function can be used to do inference on the partially identified parameter maintaining the point identification conditions we propose a quantile minimum distance estimator which converges at the parametric rate to the parameter vector of interest and has an asymptotically normal distribution a small scale simulation study and an application using drug relapse data demonstrate satisfactory finite sample performance

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

semiparametric estimation of the random utility model with rank ordered choice data abstract we propose semiparametric methods for estimating random utility models using rank ordered choice data our primary method is the generalized maximum score gms estimator with partially rank ordered data the gms estimator allows for arbitrary forms of interpersonal heteroskedasticity with fully rank ordered data the gms estimator becomes considerably more flexible allowing for random coefficients and alternative specific heteroskedasticity and correlations the gms estimator has a non standard asymptotic distribution and a convergence rate of n 1 3 we proceed to construct its smoothed version which is asymptotically normal with a faster convergence rate of n d 2 d 1 where d 2 increases in the strength of smoothness assumptions

direct semiparametric estimation of single index models with discrete covariates abstract others have developed average derivative estimators of the parameter in the model e y x x g x where g is an unknown function and x is a random vector these estimators are noniterative and easy to compute but require that x be continuously distributed this article develops a noniterative easily computed estimator of for models in which some components of x are discrete the estimator is n consistent and asymptotically normal an application to data on product innovation by german manufacturers illustrates the estimator s usefulness

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

identifying the average treatment effect in ordered treatment models without unconfoundedness we show identification of the average treatment effect ate when treatment is specified by ordered choice in cross section or panel models treatment is determined by location of a latent variable containing a continuous instrument relative to two or more thresholds we place no functional form restrictions on latent errors and potential outcomes unconfoundedness of treatment does not hold and identification at infinity for the treated is not possible yet we still show nonparametric point identification and estimation of the ate we apply our model to reinvestigate the inverted u relationship between competition and innovation and find no inverted u in us data

semiparametric estimation of a work trip mode choice model abstract a binary response model of choice between automobile and transit for travel to work is estimated using fixed and random coefficients probit specifications a semiparametric single index specification and a semiparametric specification that permits arbitrary heteroskedasticity of unknown form the estimation methods are maximum likelihood for the probit models semiparametric quasi maximum likelihood for the single index model and maximum score and smoothed maximum score for the arbitrarily heteroskedastic model specification tests result in rejection of the fixed coefficients probit and single index models but not of the random coefficients probit model and the semiparametric model with arbitrary heteroskedasticity

the random coefficients logit model is identified the random coecients multinomial choice logit model also known as the mixed logit has been widely used in empirical choice analysis for the last thirty years we prove that the distribution of random coecients in the multinomial logit model is nonparametrically identified

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

endogenous selection or treatment model estimation in a sample selection or treatment effects model common unobservables may affect both the outcome and the probability of selection in unknown ways this paper shows that the distribution function of potential outcomes conditional on covariates can be identified given an observed variable v that affects the treatment or selection probability in certain ways and is conditionally independent of the error terms in a model of potential outcomes selection model estimators based on this identification are provided which take the form of simple weighted averages gmm or two stage least squares these estimators permit endogenous and mismeasured regressors empirical applications are provided to estimation of a firm investment model and a schooling effects on wages model

a simple ordered data estimator for inverse density weighted expectations abstract we consider estimation of means of functions that are scaled by an unknown density or equivalently integrals of conditional expectations the ordered data estimator we provide is root n consistent asymptotically normal and is numerically extremely simple involving little more than ordering the data and summing the results no sample size dependent smoothing is required a similarly simple estimator is provided for the limiting variance the proofs include new limiting distribution results for functions of nearest neighbor spacings potential applications include endogenous binary choice willingness to pay selection and treatment models

bayesian estimation of the average treatment effect on the treated using inverse weighting we develop a bayesian approach to estimate the average treatment effect on the treated in the presence of confounding the approach builds on developments proposed by saarela et al in the context of marginal structural models using importance sampling weights to adjust for confounding and estimate a causal effect the bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in bayesian causal estimation relying on a joint likelihood we present results from simulation studies to estimate the average treatment effect on the treated evaluating the impact of sample size and the strength of confounding on estimation we illustrate our approach using the classic right heart catheterization data set and find a negative causal effect of the exposure on 30 day survival in accordance with previous analyses of these data we also apply our approach to the data set of the national center for health statistics birth data and obtain a negative effect of maternal smoking during pregnancy on birth weight

moment conditions and bayesian non parametrics models phrased through moment conditions are central to much of modern inference here these moment conditions are embedded within a non parametric bayesian set up handling such a model is not probabilistically straightforward as the posterior has support on a manifold we solve the relevant issues building new probability and computational tools by using hausdorff measures to analyse them on real and simulated data these new methods which involve simulating on a manifold can be applied widely including providing bayesian analysis of quasi likelihoods linear and non linear regression missing data and hierarchical models

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

binary response correlated random coefficient panel data models abstract in this paper we consider binary response correlated random coefficient crc panel data models which are frequently used in the analysis of treatment effects and demand of products we focus on the nonparametric identification and estimation of panel data models under unobserved heterogeneity which is captured by random coefficients and when these random coefficients are correlated with regressors our identification conditions and estimation are based on the framework of the model with a special regressor which is a novel approach proposed by lewbel 1998 lewbel 2000 to solve the heterogeneity and endogeneity problem in the binary response models with the help of the additional information on the special regressor we can transform a binary response crc model to a linear moment relation we also construct a semiparametric estimator for the average slopes and derive the n normality result further we propose a nonparametric method to test the correlations between random coefficients and regressors simulations are given to show the finite sample performance of our estimators and test statistics

heterogeneous treatment effects instrumental variables without monotonicity imbens and angrist 1994 were the first to exploit a monotonicity condition in order to identify a local average treatment effect parameter using instrumental variables more recently heckman and vytlacil 1999 suggested the estimation of a variety of treatment effect parameters using a local version of their approach we investigate the sensitivity of the respective estimates to random departures from monotonicity approximations to the respective bias terms are derived in an empirical application the bias is calculated and bias corrected estimates are obtained the accuracy of the approximation is investigated in a monte carlo study

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

an application of harrell s c index to ph frailty models frailty models are encountered in many medical applications yet little research has been devoted to develop measures that quantify the predictive ability of these models in this paper we elaborate on the concept of the concordance probability to clustered data resulting in an overall conditional c index or bfc o c and an overall marginal c index or c o m both overall c indices can be split up into a between conditional or c b c and a between marginal c index or c b m and into a within conditional or c w c and a within marginal c index or c w m for ph frailty models of the power variance family c w c and c w m are equivalent resulting in one within c index c w we propose an application of harrell s c index to estimate the proposed indices within a likelihood and a bayesian context and the performances of their point estimates and confidence credible intervals are compared in an extensive simulation study this simulation study shows that the point estimates of c w and c b m perform good within both a likelihood and bayesian context but that the point estimates of c b c show less bias for the bayesian approach than for the likelihood approach the 95 per cent confidence credible intervals also possess good coverage properties given that the point estimates perform good the performance of the c indices is evaluated on a real data set

exact multivariate bayesian bootstrap distributions of moments the common unknown probability law p of a random sample y 1 y n is assigned a dirichlet process prior with index it is shown that the posterior joint density of several moments of p converges as r 0 to a multivariate b spline which is therefore the bayesian bootstrap joint density of the moments the result provides the basis for possible default nonparametric bayesian inference on unknown moments

a poisson mixture model of discrete choice abstract in this paper we introduce a new poisson mixture model for count panel data where the underlying poisson process intensity is determined endogenously by consumer latent utility maximization over a set of choice alternatives this formulation accommodates the choice and count in a single random utility framework with desirable theoretical properties individual heterogeneity is introduced through a random coefficient scheme with a flexible semiparametric distribution we deal with the analytical intractability of the resulting mixture by recasting the model as an embedding of infinite sequences of scaled moments of the mixing distribution and newly derive their cumulant representations along with bounds on their rate of numerical convergence we further develop an efficient recursive algorithm for fast evaluation of the model likelihood within a bayesian gibbs sampling scheme we apply our model to a recent household panel of supermarket visit counts we estimate the nonparametric density of three key variables of interest price driving distance and their interaction while controlling for a range of consumer demographic characteristics we use this econometric framework to assess the opportunity cost of time and analyze the interaction between store choice trip frequency search intensity and household and store characteristics we also conduct a counterfactual welfare experiment and compute the compensating variation for a 10 30 increase in walmart prices

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

dynamic treatment effects this paper develops robust models for estimating and interpreting treatment effects arising from both ordered and unordered multi stage decision problems identification is secured through instrumental variables and or conditional independence matching assumptions we decompose treatment effects into direct effects and continuation values associated with moving to the next stage of a decision problem using our framework we decompose the iv estimator showing that iv generally does not estimate economically interpretable or policy relevant parameters in prototypical dynamic discrete choice models unless policy variables are instruments continuation values are an empirically important component of estimated total treatment effects of education we use our analysis to estimate the components of what late estimates in a dynamic discrete choice model

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

maps preserving semi fredholm operators on hilbert c modules abstract let m be a hilbert c module over the c algebra a and l a m the c algebra of all adjointable operators on m let l a m l a m be a unital linear map preserving semi a fredholm operators in both directions and assume that is surjective up to compact operators we will show that preserves compact operators and in certain cases the induced map l a m k a m l a m k a m is an automorphism or an anti automorphism

bayesian nonparametric analysis of longitudinal studies in the presence of informative missingness summaryin longitudinal clinical trials one often encounters missingness that is thought to be nonignorable such missingness introduces identifiability issues resulting in causal effects being nonparametrically unidentified it is then prudent to conduct a sensitivity analysis to assess how much of the inference is being driven by untestable assumptions needed to identify the effects of interest we introduce a bayesian nonparametric framework for conducting inference in the presence of nonignorable nonmonotone missingness this framework focuses on the specification of an auxiliary working prior on the space of complete data generating mechanisms this prior induces a prior on the observed data generating mechanism which is then used in conjunction with an identifying restriction to conduct inference advantages of this approach include a flexible modelling framework access to simple computational methods strong theoretical support straightforward sensitivity analysis and applicability to nonmonotone missingness

bayesian exponentially tilted empirical likelihood summary while empirical likelihood has been shown to exhibit many of the properties of conven tional parametric likelihoods a formal probabilistic interpretation has so far been lacking we show that a likelihood function very closely related to empirical likelihood naturally arises from a nonparametric bayesian procedure which places a type of noninformative prior on the space of distributions this prior gives preference to distributions having a small support and among those sharing the same support it favours entropy maximising distributions the resulting nonparametric bayesian procedure admits a computationally convenient representation as an empirical likelihood type likelihood where the probability weights are obtained via exponential tilting the proposed methodology provides an attractive alternative to the bayesian bootstrap as a nonparametric limit of a bayesian procedure for moment condition models

consistent nonparametric hypothesis tests with an application to slutsky symmetry abstract a general consistent nonparametric testing technique is applied to u k survey data to test slutsky symmetry this paper first provides a set of low level technical assumptions that yield root n convergence of averages of functions of both kernel estimators and their derivatives the results are then used to construct nonparametric moment based tests including the extension to consistent tests i e tests that asymptotically have correct size and have power against all relevant alternatives the nonparametric tests are compared to ordinary parametric tests from the quaids quadratic almost ideal demand system functional form

case control studies with contaminated controls abstract this paper considers inference about a parametric binary choice model when the data consist of two distinct samples the first is a random sample from the people who made choice 1 say with all relevant covariates completely observed the second is a random sample from the whole population with only the covariates observed this is called a contaminated sampling scheme an example might be where we have a random sample of female labor force participants and their covariate values and a second random sample of working age women with covariates whose participant status is unknown we consider the cases in which the fraction of the population making choice 1 is known and that in which it is not for both cases we give semiparametrically efficient procedures for estimating the choice model parameters

the repeated insertion model for rankings missing link between two subset choice models several probabilistic models for subset choice have been proposed in the literature for example to explain approval voting data we show that marley et al s latent scale model is subsumed by falmagne and regenwetter s size independent model in the sense that every choice probability distribution generated by the former can also be explained by the latter our proof relies on the construction of a probabilistic ranking model which we label the repeated insertion model this model is a special case of marden s orthogonal contrast model class and in turn includes the classical mallows model as a special case we explore its basic properties as well as its relationship to fligner and verducci s multistage ranking model

the bayesian bootstrap the bayesian bootstrap is the bayesian analogue of the bootstrap instead of simulating the sampling distribution of a statistic estimating a parameter the bayesian bootstrap simulates the posterior distribution of the parameter operationally and inferentially the methods are quite similar because both methods of drawing inferences are based on somewhat peculiar model assumptions and the resulting inferences are generally sensitive to these assumptions neither method should be applied without some consideration of the reasonableness of these model assumptions in this sense neither method is a true bootstrap procedure yielding inferences unaided by external assumptions

excess heterogeneity endogeneity and index restrictions a discrete or continuous outcome is determined by a structural function in which the effect of some variables of interest is transmitted through a scalar index multiple sources of stochastic variation can appear as arguments of the structural function but not in the index there may be endogeneity that is observable and unobservable variables may not be independently distributed conditions are provided under which there is local identification of measures of the relative sensitivity of the index to variations in pairs of its possibly endogenous arguments namely ratios of partial derivatives of the index

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

the product of operators with closed range in hilbert c modules abstract suppose t and s are bounded adjointable operators with close range between hilbert c modules then ts has closed range if and only if ker t ran s is an orthogonal summand if and only if ker s ran t is an orthogonal summand moreover if the dixmier or minimal angle between ran s and ker t ker t ran s is positive and ker s ran t is an orthogonal summand then ts has closed range

semiparametric estimation of binary response models with endogenous regressors abstract in this paper we propose a two step semiparametric maximum likelihood sml estimator for the coefficients of a single index binary choice model with endogenous regressors when identification is achieved via a control function approach the first step consists of estimating a reduced form equation for the endogenous regressors and extracting the corresponding residuals in the second step the latter are added as control variates to the outcome equation which is in turn estimated by sml we establish the estimator s n consistency and asymptotic normality in a simulation study we compare the properties of our estimator with those of existing alternatives highlighting the advantages of our approach

rates of convergence for estimating regression coefficients in heteroskedastic discrete response models abstract in this paper we consider estimation of discrete response models exhibiting conditional heteroskedasticity of a multiplicative form where the latent error term is assumed to be the product of an unknown scale function and a homoskedastic error term it is first shown that for estimation of the slope coefficients in a binary choice model under this type of restriction the semiparametric information bound is zero even when the homoskedastic error term is parametrically specified hence it is impossible to attain the parametric convergence rate for the parameters of interest however for ordered response models where the response variable can take at least three different values the parameters of interest can be estimated at the parametric rate under the multiplicative heteroskedasticity assumption two estimation procedures are proposed the first estimator based on a parametric restriction on the homoskedastic component of the error term is a two step maximum likelihood estimators where the unknown scale function is estimated nonparametrically in the first stage the second procedure which does not require the parametric restriction estimates the parameters by a kernel weighted least squares procedure under regularity conditions which are standard in the literature both estimators are shown to be n consistent and asymptotically normal

bandwidth choice for average derivative estimation abstract the average derivative is the expected value of the derivative of a regression function kernel methods have been proposed as a means of estimating this quantity the problem of bandwidth selection for these kernel estimators is addressed here asymptotic representations are found for the variance and squared bias these are compared with each other to find an insightful representation for a bandwidth optimizing terms of lower order than n 1 it is interesting that for dimensions greater than 1 negative kernels have to be used to prevent domination of bias terms in the asymptotic expression of the mean squared error the extent to which the theoretical conclusions apply in practice is investigated in an economical example related to the so called law of demand

empirical likelihood for small area estimation abstract small areaestimation has become a topic of growingimportance inrecent years due to increasing demand for small area statistics fromboth the public and private sectors the current methodologies inthis area with possibly a handful of exceptions are all parametric be it bayesian or frequentist even the so called nonparamet ric procedures based on empirical best linear unbiased predictors eblup assume linearity of the estimators of small area means resampling methods like jacknife and bootstrap are used mostlyfor mean squared error estimation in this paper we propose analternative bayesian approach based on empirical likelihood whichdoes not require the assumption of either a parametric likelihoodor linearity of estimators the proposed method can also handleboth discrete and continuous data in a uni ed manner empiricallikelihood for both area and unit level models are introduced theimproved performance of our estimator is illustrated through twoexamples involving both discrete and continuous data key words and phrases area level exponentially tilted t prior unit level

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

empirical likelihood as a goodness of fit measure summary the method of empirical likelihood can be viewed as one of allocating probabilities to an n cell contingency table so as to minimise a goodness of fit criterion it is shown that when the cressie read power divergence statistic is used as the criterion confidence regions enjoying the same convergence rates as those found for empirical likelihood can be obtained for the entire range of values of the cressie read parameter including 1 maximum entropy 0 empirical likelihood and 1 pearson s z2 it is noted that in the power divergence family empirical likelihood is the only member which is bartlettcorrectable however simulation results suggest that for the mean using a scaled f distribution yields more accurate coverage levels for moderate sample sizes

identifying effects of multivalued treatments multivalued treatment models have typically been studied under restrictive assumptions ordered choice and more recently unordered monotonicity we show how treatment effects can be identified in a more general class of models that allows for multidimensional unobserved heterogeneity our results rely on two main assumptions treatment assignment must be a measurable function of threshold crossing rules and enough continuous instruments must be available we illustrate our approach for several classes of models

bayesian bootstrap estimation of roc curve receiver operating characteristic roc curve is widely applied in measuring discriminatory ability of diagnostic or prognostic tests this makes the roc analysis one of the most active research areas in medical statistics many parametric and semiparametric estimation methods have been proposed for estimating the roc curve and its functionals in this paper we propose the bayesian bootstrap bb a fully nonparametric estimation method for the roc curve and its functionals such as the area under the curve auc the bb method offers a bandwidth free smoothing approach to the empirical estimate and gives credible bounds the accuracy of the estimate of the roc curve in the simulation studies is examined by the integrated absolute error in comparison with other existing curve estimation methods the bb method performs well in terms of accuracy robustness and simplicity we also propose a procedure based on the bb approach to test the binormality assumption

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

set identified linear models we analyze the identification and estimation of parameters satisfying the incomplete linear moment restrictions e z x y e z u z where z is a set of instruments and u z an unknown bounded scalar function we first provide empirically relevant examples of such a set up second we show that these conditions set identify where the identified set b is bounded and convex we provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest but also in the case in which the number of conditions is strictly larger than the number of parameters we derive a necessary and sufficient condition of the validity of supernumerary restrictions which generalizes the familiar sargan condition third we provide new results on the asymptotics of analog estimates constructed from the identification results when b is a strictly convex set we also construct a test of the null hypothesis 0 2 b whose size is asymptotically correct and which relies on the minimization of the support function of the set b 0 results of some monte carlo experiments are presented

bayes wesml posterior inference from choice based samples abstract in this paper i show that the weighted exogenous sampling likelihood wesml estimator for choice based samples due to manski and lerman 1977 can be given a bayesian interpretation under a multinomial model for the data with improper dirichlet priors bayesian posterior distributions of choice model parameters are computed to study the gains from choice based sampling and the effect of knowledge of population marginal choice probabilities

bayesian bootstrap multivariate regression a bayesian bootstrap multivariate regression bbmr procedure is presented that allows robust bayesian analysis of multivariate regression models bbmr does not require a parametric specification for the likelihood function and instead uses a bootstrapped likelihood based on the sampling distribution of location and scale estimators a mixing algorithm for implementing the procedure automatically incorporates the scale invariant ignorance prior on the covariance matrix bbmr can be implemented as a generic algorithm in standard statistical software independently of the actual choice of prior distribution monte carlo evidence is provided showing accuracy and robustness of the approach in representing posterior distributions

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

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

bayesian moment based inference in a regression model with misclassification error we present a bayesian analysis of a regression model with a binary covariate that may have classification measurement error prior research demonstrates that the regression coefficient is only partially identified we take a bayesian approach which adds assumptions in the form of priors on the unknown misclassification probabilities the approach is intermediate between the frequentist bounds of previous literature and strong assumptions which achieve point identification and thus preferable in many settings we present two simple algorithms to sample from the posterior distribution when the likelihood function is not fully parametric but only satisfies a set of moment restrictions we focus on how varying amounts of information contained in a prior distribution on the misclassification probabilities change the posterior of the parameters of interest while the priors add information to the model they do not necessarily tighten the identified set however the information is sufficient to tighten bayesian inferences we also consider the case where the mismeasured binary regressor is endogenous we illustrate the use of our bayesian approach in a simulated data set and an empirical application investigating the association between narcotic pain reliever use and earnings

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

nonparametric identification of the distribution of random coefficients in binary response static games of complete information this paper studies binary response static games of complete information allowing complex heterogeneity through a random coefficients specification the main result of the paper establishes nonparametric point identification of the joint density of all random coefficients except those on interaction effects under additional independence assumptions we identify the joint density of the interaction coefficients moreover we prove that in the presence of covariates that are common to both players the player specific coefficient densities are identified while the joint density of all random coefficients is not point identified however we do provide bounds on counterfactual probabilities that involve this joint density

bayesian regression with nonparametric heteroskedasticity abstract this paper studies large sample properties of a semiparametric bayesian approach to inference in a linear regression model the approach is to model the distribution of the regression error term by a normal distribution with the variance that is a flexible function of covariates the main result of the paper is a semiparametric bernstein von mises theorem under misspecification even when the distribution of the regression error term is not normal the posterior distribution of the properly recentered and rescaled regression coefficients converges to a normal distribution with the zero mean and the variance equal to the semiparametric efficiency bound

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

identification and estimation of games with incomplete information using excluded regressors the existing literature on binary games with incomplete information assumes that either payo functions or the distribution of private information are nitely parameterized to obtain point identi cation in contrast we show that given excluded regressors payofunctions and the distribution of private information can both be nonparametrically point identi ed an excluded regressor for player i is a su ciently varying state variable that does not aect other players utility and is additively separable from other components in i s payo we show how excluded regressors satis fying these conditions arise in contexts such as entry games between rms as variation in observed components of xed costs our identi cation proofs are constructive so consistent nonparametric estimators can be readily based on them for a semiparametric model with linear payos we propose root n consistent and asymptotically normal estimators for parameters in players payos finally we extend our approach to accommodate the existence of multiple bayesian nash equilibria in the data generating process without assuming equilibrium selection rules

a two sample test with interval censored data via multiple imputation interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be recorded as having occurred between two examination times in this paper we consider the problem of comparing two interval censored samples we propose to impute exact failure times from interval censored observations to obtain right censored data then apply existing techniques such as harrington and fleming s g rho tests to imputed right censored data to appropriately account for variability a multiple imputation algorithm based on the approximate bayesian bootstrap abb is discussed through simulation studies we find that it performs well the advantage of our proposal is its simplicity to implement and adaptability to incorporate many existing two sample comparison techniques for right censored data the method is illustrated by reanalysing the breast cosmesis study data set

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

some general techniques on linear preserver problems abstract several general techniques on linear preserver problems are described the first one is based on a transfer principle in model theoretic algebra that allows one to extend linear preserver results on complex matrices to matrices over other algebraically closed fields of characteristic 0 the second one concerns the use of some simple geometric technique to reduce linear preserver problems to standard types so that known results can be applied the third one is about solving linear preserver problems on more general operator algebras by reducing the problems to idempotent preservers numerous examples will be given to demonstrate the proposed techniques