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

set identification via quantile restrictions in short panels this paper studies the identifying power of conditional quantile restrictions in short panels with flxed efiects in contrast to classical flxed efiects models with conditional mean restrictions conditional quantile restrictions are not preserved by taking difierences in the regression equation over time this paper shows however that a conditional quantile restriction in conjunction with a weak conditional independence restriction provides bounds on quantiles of difierences in time varying unobservables across periods these bounds carry observable implications for model parameters which generally result in set identiflcation the analysis of these bounds includes conditions for point identiflcation of the parameter vector as well as weaker conditions that result in identiflcation of individual parameter components

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

on certain polynomial time truth table reducibilities of complete sets to sparse sets let sigma be a finite alphabet a set s subset sigma is called sparse if the number of members of s having length at most n is bounded above by a polynomial in n let leqq m p denote polynomial time many one reducibility and let leqq bptt p denote the more general polynomial time bounded positive truth table reducibility we prove 1 leqq bptt p reducibility of a conp hard set to a sparse set implies text np text p and 2 leqq bptt p reducibility of an np hard set to a sparse set which is itself in np implies text np text p 1 generalizes fortune s result f he proved it for the case of leqq m p reducibility 2 for the case of leqq m p reducibility was proved by mahaney m even without assuming that the sparse set itself is in np our results imply that if a conp hard set is a finite union of sets which are leqq m p reducible to sparse sets then text np text p we then investigate a certain non

semiparametric estimation of censored selection models with a nonparametric selection mechanism abstract in this paper estimation of the coefficients in a single index selectivity bias model is considered under the assumption that the selection correction function depends on the conditional mean of some observable selection variable the estimation method follows a familiar two step strategy the first step uses a nonparametric regression estimator for the selection variable while the second step uses a weighted instrumental variables estimator for the coefficients in the equation of interest the paper gives conditions under which the proposed estimator is root n consistent and asymptotically normal the proposed method is applied to data on labor supply

identification and nonparametric estimation of a transformed additively separable model let r x z be a function that along with its derivatives can be consistently estimated nonparametrically this paper discusses the identification and consistent estimation of the unknown functions h m g and f where r x z h m x z m x z g x f z and h is strictly monotonic an estimation algorithm is proposed for each of the model s unknown components when r x z represents a conditional mean function the resulting estimators use marginal integration to separate the components g and f our estimators are shown to have a limiting normal distribution with a faster rate of convergence than unrestricted nonparametric alternatives their small sample performance is studied in a monte carlo experiment we apply our results to estimate generalized homothetic production functions for four industries in the chinese economy

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

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

breaking the curse of dimensionality in conditional moment inequalities for discrete choice models abstract this paper studies inference of preference parameters in semiparametric discrete choice models when these parameters are not point identified and the identified set is characterized by a class of conditional moment inequalities exploring the semiparametric modeling restrictions we show that the identified set can be equivalently formulated by moment inequalities conditional on only two continuous indexing variables such formulation holds regardless of the covariate dimension thereby breaking the curse of dimensionality for nonparametric inference based on the underlying conditional moment inequalities we further apply this dimension reducing characterization approach to the monotone single index model and to a variety of semiparametric models under which the sign of conditional expectation of a certain transformation of the outcome is the same as that of the indexing variable

general single index survival regression models for incident and prevalent covariate data and prevalent data without follow up this article mainly focuses on analyzing covariate data from incident and prevalent cohort studies and a prevalent sample with only baseline covariates of interest and truncation times our major task in both research streams is to identify the effects of covariates on a failure time through very general single index survival regression models without observing survival outcomes with a strict increase of the survival function in the linear predictor the ratio of incident and prevalent covariate densities is shown to be a non degenerate and monotonic function of the linear predictor under covariate independent truncation without such a structural assumption the conditional density of a truncation time in a prevalent cohort is ensured to be a non degenerate function of the linear predictor in light of these features some innovative approaches which are based on the maximum rank correlation estimation or the pseudo least integrated squares estimation are developed to estimate the coefficients of covariates up to a scale factor existing theoretical results are further used to establish the n consistency and asymptotic normality of the proposed estimators moreover extensive simulations are conducted to assess and compare the finite sample performance of various estimators to illustrate the methodological ideas we also analyze data from the worcester heart attack study and the national comorbidity survey replication

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

a unified approach to semiparametric transformation models under general biased sampling schemes we propose a unified estimation method for semiparametric linear transformation models under general biased sampling schemes the new estimator is obtained from a set of counting process based unbiased estimating equations developed through introducing a general weighting scheme that offsets the sampling bias the usual asymptotic properties including consistency and asymptotic normality are established under suitable regularity conditions a closed form formula is derived for the limiting variance and the plug in estimator is shown to be consistent we demonstrate the unified approach through the special cases of left truncation length bias the case cohort design and variants thereof simulation studies and applications to real datasets are presented

convergence in a quasilinear parabolic equation with time almost periodic boundary conditions abstract consider the problem u t a u x u x x f u x x 1 t 0 u x 1 t g t t 0 where g t is an almost periodic function we prove the following convergence results if a time global solution u is bounded then it converges to an almost periodic solution which is unique up to space shift stable and asymptotically stable if u goes to infinity with positive lower average speed then it converges to an almost periodic traveling wave which is unique up to space shift stable asymptotically stable and has positive average speed

probabilistic index models summary we present a semiparametric statistical model for the probabilistic index which can be defined as p y y a where y and y a are independent random response variables associated with covariate patterns x and x a respectively a link function defines the relationship between the probabilistic index and a linear predictor asymptotic normality of the estimators and consistency of the covariance matrix estimator are established through semiparametric theory the model is illustrated with several examples and the estimation theory is validated in a simulation study

convergence in a quasilinear parabolic equation with neumann boundary conditions abstract consider the problem u t a u x u x x f u x x 1 t 0 u x 1 t k t u 1 t t 0 where k are smooth functions which are periodic in both t and u brunovsk et al proved in their paper brunovsk et al 1992 8 that if a time global solution u is bounded then it converges to a periodic solution we prove that if u is unbounded from above then it converges to a periodic traveling wave v x t c t in case k k t or k k u where v is a time periodic function and c 0 in addition the periodic traveling wave is unique up to space shifts or time shifts it is stable and asymptotically stable the average traveling speed c and the instantaneous speed v t c are also studied

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

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

testing for threshold effects in regression models in this article we develop a general method for testing threshold effects in regression models using sup likelihood ratio lr type statistics although the sup lr type test statistic has been considered in the literature our method for establishing the asymptotic null distribution is new and nonstandard the standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function the article provides an alternative novel method that can be used to establish the asymptotic null distribution even when the usual quadratic approximation is intractable we illustrate the usefulness of our approach in the examples of the maximum score estimation maximum likelihood estimation quantile regression and maximum rank correlation estimation we establish consistency and local power properties of the test we provide some simulation results and also an empirical application to tipping in racial segregation this ar

on prediction and the power transformation family summary the power transformation family is often used for transforming to a normal linear model the variance of the regression parameter estimators can be much larger when the transformation parameter is unknown and must be estimated compared to when the transformation parameter is known we consider prediction of future untransformed observations when the data can be transformed to a linear model when the transformation must be estimated the prediction error is not much larger than when the parameter is known

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

dct qm a dct based quality degradation metric for image quality optimization problems recent development of computational image quality assessment methods has shown to give very promising results in measuring perceptual visual quality for distorted images however most of them are difficult to be applied for optimization problems due to the lack of desirable mathematical properties such as differentiability convexity and valid distance metricability this paper proposes a novel discrete cosine transform dct based quality degradation metric called dct qm which is based on the probability summation theory with a psychometric function for neural responses in the receptive fields of visual cortex in psychophysics consequently the dct qm is formulated as a weighted mean text l 2 norm in the dct domain which is very easy to implement and inherits the three desirable mathematical properties that is differentiability convexity and valid distance metricability for image quality optimization problems the extensive experimental results show that the proposed dct qm has promising results for many practical distortion types in image processing problems by showing high consistency with perceived visual quality

semiparametric estimation of a proportional hazard model with unobserved heterogeneity the proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity this paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically the baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known finite dimensional parametric families existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family thus the estimators presented here are more general than existing ones

the analysis of transformed data abstract recently it was suggested bickel and doksum 1981 that when data are used to select a transformation the post transformation analysis of those data may need to be modified considerably from standard form so as to allow for the selection we argue that common sense and the work of box and cox 1964 point to a contrary conclusion our argument is based on considerations of parameter interpretation and subsequent bayesian analysis within the context of fitting normal error linear models numerical examples are used to illustrate the main points

partial rank estimation of duration models with general forms of censoring abstract in this paper we propose estimators for the regression coefficients in censored duration models which are distribution free impose no parametric specification on the baseline hazard function and can accommodate general forms of censoring the estimators are shown to have desirable asymptotic properties and monte carlo simulations demonstrate good finite sample performance among the data features the new estimators can accommodate are covariate dependent censoring double censoring and fixed individual or group specific effects we also examine the behavior of the estimator in an empirical illustration

two stage rank estimation of quantile index models abstract this paper estimates a class of models which satisfy a monotonicity condition on the conditional quantile function of the response variable this class includes as a special case the monotonic transformation model with the error term satisfying a conditional quantile restriction thus allowing for very general forms of conditional heteroscedasticity a two stage approach is adopted to estimate the relevant parameters in the first stage the conditional quantile function is estimated nonparametrically by the local polynomial estimator discussed in chaudhuri journal of multivariate analysis 39 1991a 246 269 annals of statistics 19 1991b 760 777 and cavanagh 1996 preprint in the second stage the monotonicity of the quantile function is exploited to estimate the parameters of interest by maximizing a rank based objective function the proposed estimator is shown to have desirable asymptotic properties and can then also be used for dimensionality reduction or to estimate the unknown structural function in the context of a transformation model

on symmetric differences of np hard sets with weakly p selective sets the symmetric differences of np hard sets with weakly p selective sets are investigated we show that if there exist a weakly p selective set a and an np pm hard set h such that h a pbtt sparse and a h pm sparse then p np so no np pm hard set has sparse symmetric difference with any weakly p selective set unless p np the proof of our main result is an interesting application of the tree prunning techniques fortune 1979 mahaney 1982 in addition we show that there exists a p selective set which has exponentially dense symmetric difference with every set in pbtt sparse

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

rank estimators for monotonic index models we present a new class of rank estimators of scaled coefficients in semiparametric monotonic linear index models the estimators require no subjective bandwidth choices and have attractive computational properties we establish n consistency and asymptotic normality and provide the general form and consistent estimators of the asymptotic covariance matrix we also provide a generalization covering single equation multiple indices models satisfying certain monotonicity constraints an analogue of consistency when all explanatory variables are categorical is established and an application is presented

misspecified nonconvex statistical optimization for sparse phase retrieval existing nonconvex statistical optimization theory and methods crucially rely on the correct specification of the underlying true statistical models to address this issue we take a first step towards taming model misspecification by studying the high dimensional sparse phase retrieval problem with misspecified link functions in particular we propose a simple variant of the thresholded wirtinger flow algorithm that given a proper initialization linearly converges to an estimator with optimal statistical accuracy for a broad family of unknown link functions we further provide extensive numerical experiments to support our theoretical findings

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

the limiting distribution of the maximum rank correlation estimator han s maximum rank correlation mrc estimator is shown to be 4 consistent and asymptotically normal the proof rests on a general method for determining the asymptotic distribution of a maximization estimator a simple u statistic decomposition and a uniform bound for degenerate u processes a consistent estimator of the asymptotic covariance matrix is provided along with a result giving the explicit form of this matrix for any model within the scope of the mrc estimator the latter result is applied to the binary choice model and it is found that the mrc estimator does not achieve the semiparametric efficiency bound

non parametric analysis of a generalized regression model the maximum rank correlation estimator the paper considers estimation of a model yi d f x i 0 ui where the composite transformation d f is only specified that d r r is non degenerate monotonic and f r2 r is strictly monotonic in each of its variables the paper thus generalizes standard data analysis which assumes that the functional form of d f is known and additive the estimator which it proposes is the maximum rank correlation estimator which is non parametric in the functional form of d f and non parametric in the distribution of the error terms ui the estimator is shown to be strongly consistent for the parameters 0 up to a scale coefficient

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

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

an extension of the proportional hazards model for grouped data summary a family of transformations for probabilities is considered for the analysis of grouped survival data additive and multiplicative models for the hazard function are compared a method is suggested for estimating the scale on which an additive representation of the hazard in terms of explanatory variables is appropriate computations are performed using glim a test for departures from the grouped proportional hazards model is introduced an example is analyzed by the methods put forward in the analysis of survival data the effects of explanatory variables on failure time t are of great interest these effects are perhaps most conveniently investigated by establishing simple models for the hazard function in terms of explanatory variables we focus attention on additive and multiplicative models for the hazard the approach taken is to analyze sequences of contingency tables constructed from the data this follows mantel 1966 though the way in which we determine the sequences parallels work by holford 1976 certain similarities to problems involving binary data are exploited in particular a family of transformations for probabilities is defined which includes both additive and multiplicative models as special cases generalized linear models nelder and wedderburn 1972 associated with the transformations may be tried on the data and their fits compared in 3 a test for departures from the grouped multiplicative model in the direction of the grouped additive model is proposed and the forms of two simple estimates of the survivor function are given the methods are applied to an example in 4

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

rank estimation of a generalized fixed effects regression model abstract this paper considers estimation of a fixed effects version of the generalized regression model of han 1987 journal of econometrics 35 303 316 the model allows for censoring places no parametric assumptions on the error disturbances and allows the fixed effects to be correlated with the covariates we introduce a class of rank estimators that consistently estimate the coefficients in the generalized fixed effects regression model the maximum score estimator for the binary choice fixed effects model is part of this class like the maximum score estimator the class of rank estimators converge at less than the n rate smoothed versions of these estimators however converge at rates approaching the n rate in a version of the model that allows for truncated data a sufficient condition for consistency of the estimators is that the error disturbances have an increasing hazard function

reductions on np and p selective sets abstract p selective sets are used to distinguish polynomial time bounded reducibilities on np in particular we consider different kinds of positive reductions these preserve membership in np and are not a priori closed under complements we show that the class of all sets which are both p selective and have positive reductions to their complements is p this is used to show that if dext next then there exists a set in np p that is not positive reducible to its complement various similar results are obtained we also show that p is the class of all sets which are both p selective and positive truth table self reducible from this result it follows that various naturally defined apparently intractible problems are not p selective unless p np

maximal inequalities for degenerate u processes with applications to optimization estimators maximal inequalities for degenerate u processes of order k k geq 1 are established the results rest on a moment inequality due to bonami for k th order forms and on extensions of chaining and symmetrization inequalities from the theory of empirical processes rates of uniform convergence are obtained the maximal inequalities can be used to determine the limiting distribution of estimators that optimize criterion functions having u process structure as an application a semiparametric regression estimator that maximizes a u process of order 3 is shown to be sqrt n consistent and asymptotically normally distributed

on sets truth table reducible to sparse sets we study sets that are truth table reducible to sparse sets in polynomial time the principal results are as follows 1 for every integer k 0 there is a set l and a sparse set s such that l

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

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 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

linear regression with interval censored data i occurred in reliability studies destructive tests are often used to find whether an item e g fire extinguisher has failed in rodent bioassay experiments the presence or absence of a tumor may only be detected through sacrifices for certain designs of experiments t are i i d random variables with a i known probability density in general t and z are associated in case 2 ii interval censoring two censoring variables t t are observed with the ii knowledge that y is inside the interval t t in both cases of interval ii i

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

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

semiparametrically efficient inference based on signs and ranks for median restricted models since the pioneering work of koenker and bassett 1978 econometric models involving median and quantile rather than the classical mean or conditional mean concepts have attracted much interest contrary to the traditional models where the noise is assumed to have mean zero median restricted models enjoy a rich group invariance structure in this paper we exploit this invariance structure in order to obtain semiparametrically efficient inference procedures for these models these procedures are based on residual signs and ranks and therefore insensitive to possible misspecification of the underlying innovation density yet semiparametrically efficient at correctly specified densities this latter combination is a definite advantage of these procedures over classical quasi likelihood methods the techniques we propose can be applied without additional technical difficulties to both cross sectional and time series models they do not require any explicit tangent space calculation nor any projections on these

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

robust rank estimation for transformation models with random effects summarysemiparametric transformation models with random effects are useful in analysing recurrent and clustered data with specified error and random effect distributions zeng lin 2007a proved that nonparametric maximum likelihood estimators are semiparametric efficient in this paper we consider a more general class of transformation models with random effects under which an unknown monotonic transformation of the response is linearly related to the covariates and the random effects with unspecified error and random effect distributions this includes many popular models we propose an estimator based on the maximum rank correlation which relies on symmetry of the random effect distribution and establish its consistency and asymptotic normality a random weighting resampling scheme is employed for inference the proposed method can be extended to censored and clustered data numerical studies demonstrate that the proposed method performs well in practical situations application of the method is illustrated with the framingham cholesterol data

combining predictors for classification using the area under the receiver operating characteristic curve no single biomarker for cancer is considered adequately sensitive and specific for cancer screening it is expected that the results of multiple markers will need to be combined in order to yield adequately accurate classification typically the objective function that is optimized for combining markers is the likelihood function in this article we consider an alternative objective function the area under the empirical receiver operating characteristic curve auc we note that it yields consistent estimates of parameters in a generalized linear model for the risk score but does not require specifying the link function like logistic regression it yields consistent estimation with case control or cohort data simulation studies suggest that auc based classification scores have performance comparable with logistic likelihood based scores when the logistic regression model holds analysis of data from a proteomics biomarker study shows that performance can be far superior to logistic regression derived scores when the logistic regression model does not hold model fitting by maximizing the auc rather than the likelihood should be considered when the goal is to derive a marker combination score for classification or prediction

n prediction of generalized heteroscedastic transformation regression models abstract chen 2010 and khan 2001 consider quantile regression estimation subject to general transformation that permits general heteroscedasticity but the resulting conditional quantile predictors converge at rates slower than the parametric rate in this paper we consider the estimation of a general transformation model subject to a multiplicative form of heteroscedasticity our estimators for the finite dimensional parameters the transformation function and the resulting conditional quantile predictor all converge at the parametric rate monte carlo simulation experiments show that our estimators and conditional quantile predictor perform well in finite samples

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

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

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

two stage least absolute deviations estimators1 in this paper the method of least absolute deviations is applied to the estimation of the parameters of a structural equation in the simultaneous equations model a class of estimators called two stage least absolute deviations estimators is defined their asymptotic properties are derived and the problem of finding the optimal member of the class is considered in this paper we apply the method of least absolute deviations to the estimation of the parameters of a structural equation in the simultaneous equations model we define a class of estimators called two stage least absolute deviations estimators 2slad and derive their asymptotic properties they are so named as their relationship to the two stage least squares estimator 2sls is analogous to the relationship of the least absolute deviations estimator lad to the least squares estimator ls in the standard regression model the lad estimation has been extensively studied in the context of the standard regression model and its usefulness is universally recognized in this paper we show that the advantage of 2slad over 2sls in the simultaneous equations model can be as great as that of lad over ls in the standard regression model if 2slad is properly defined this last clause is very important since the results of this paper indicate that the lad analogue of 2sls that has been considered before in the literature is not an appropriate method

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

on rank estimators in increasing dimensions abstract the family of rank estimators including han s maximum rank correlation han 1987 as a notable example has been widely exploited in studying regression problems for these estimators although the linear index is introduced for alleviating the impact of dimensionality the effect of large dimension on inference is rarely studied this paper fills this gap via studying the statistical properties of a larger family of m estimators whose objective functions are formulated as u processes and may be discontinuous in increasing dimension set up where the number of parameters p n in the model is allowed to increase with the sample size n first we find that often in estimation as p n n 0 p n n 1 2 rate of convergence is obtainable second we establish bahadur type bounds and study the validity of normal approximation which we find often requires a much stronger scaling requirement than p n 2 n 0 third we state conditions under which the numerical derivative estimator of asymptotic covariance matrix is consistent and show that the step size in implementing the covariance estimator has to be adjusted with respect to p n all theoretical results are further backed up by simulation studies

combining multiple markers for classification using roc summary in biomedical studies it is of great interest to develop methodologies for combining multiple markers for the purpose of disease classification the receiving operating characteristic roc technique has been widely used where classification performance can be measured with the area under the roc curve auc in this article we study a roc based method for effectively combining multiple markers for disease classification we propose a sigmoid auc sauc estimator that maximizes the sigmoid approximation of the empirical auc the sauc estimator is computationally affordable n1 2 consistent and achieves the same asymptotic efficiency as the auc estimator inference based on the weighted bootstrap is investigated we also propose monte carlo methods to assess the overall prediction performance and the relative importance of individual markers finite sample performance is evaluated using simulation studies and two public data sets

roc representation for the discriminability of multi classification markers in this paper the receiver operating characteristic roc representation and its accuracy measures are well defined and meaningful assessments for the discriminability of multi classification markers are shown given a set of classifiers c a parameterized system can be used to characterize the corresponding optimal roc manifold a connection with the decision set further leads to a better understanding of some geometric features of optimal roc manifolds and preserves the simplicity in computing the hypervolume under the roc manifold hum in addition it motivates us to address the necessary and sufficient conditions for the existence of the hum to sum up this work provides working scientists with an extension of the two class roc analysis to the multi classification roc analysis in a theoretically sound manner highlightsa proper assessment of performance probabilities is shown to be the optimal roc manifold the necessary and sufficient conditions are addressed for the existence of the hum the scientific groundwork is extended to a more general multi class roc analysis

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

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

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

prediction and power transformations when the choice of power is restricted to a finite set abstract we study the family of power transformations proposed by box and cox 1964 when the choice of the power parameter is restricted to a finite set r the behavior of the box cox procedure is as anticipated in two extreme cases when the true parameter is an element of r and when is far from r we study the case in which 0 is close to r finding that the resulting methods can be very different from unrestricted maximum likelihood and that inferences may depend on the design the values of the regression parameters and the distance of to r

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

homogenization limit of a parabolic equation with nonlinear boundary conditions abstract consider the parabolic equation e u t a u x u x x f u x 1 x 1 t 0 with nonlinear boundary conditions u x 1 t g u 1 t e nbc u x 1 t g u 1 t e where e 0 is a parameter g is a function which takes values near its supremum frequently each almost periodic function is a special example of g we consider a time global solution u e of e nbc and show that its homogenization limit as e 0 is the solution of e with linear boundary conditions lbc x 1 t sup g x 1 t sup g provided moves upward monotonically when g is almost periodic lou preprint 21 obtained the unique almost periodic traveling wave u e of e nbc this paper proves that the homogenization limit of u e is a classical traveling wave of e lbc

combining biomarkers linearly and nonlinearly for classification using the area under the roc curve in biomedical studies it is often of interest to classify predict a subject s disease status based on a variety of biomarker measurements a commonly used classification criterion is based on area under the receiver operating characteristic curve auc many methods have been proposed to optimize approximated empirical auc criteria but there are two limitations to the existing methods first most methods are only designed to find the best linear combination of biomarkers which may not perform well when there is strong nonlinearity in the data second many existing linear combination methods use gradient based algorithms to find the best marker combination which often result in suboptimal local solutions in this paper we address these two problems by proposing a new kernel based auc optimization method called ramp auc rauc this method approximates the empirical auc loss function with a ramp function and finds the best combination by a difference of convex functions algorithm we show that as a linear combination method rauc leads to a consistent and asymptotically normal estimator of the linear marker combination when the data are generated from a semiparametric generalized linear model just as the smoothed auc method through simulation studies and real data examples we demonstrate that rauc outperforms smooth auc in finding the best linear marker combinations and can successfully capture nonlinear pattern in the data to achieve better classification performance we illustrate our method with a dataset from a recent hiv vaccine trial copyright 2016 john wiley sons ltd

distribution theory for the analysis of binary choice under uncertainty with nonparametric estimation of expectations abstract in analyzing discrete choice under uncertainty the practice has been to specify expectations and preferences up to a finite dimensional parameter recently manski proved the consistency of a two stage semiparametric estimator applicable if expectations are fulfilled and are conditioned only on variables observed by the researcher the first stage estimates expectations nonparametrically and the second stage uses choice data and the expectations estimate to make parametric quasi maximum likelihood inference on preferences this paper proves that the estimate of preference parameters converges at rate n to a limiting normal distribution if the expectations estimate is chosen appropriately the estimate is n asymptotically unbiased its asymptotic variance exceeds the inverted fisher information for the preference parameter

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