estimating censored regression models in the presence of nonparametric multiplicative heteroskedasticity abstract powell s 1984 journal of econometrics 25 303 325 censored least absolute deviations clad estimator for the censored linear regression model has been regarded as a desirable alternative to maximum likelihood estimation methods due to its robustness to conditional heteroskedasticity and distributional misspecification of the error term however the clad estimation procedure has failed in certain empirical applications due to the restrictive nature of the full rank condition it requires this condition can be especially problematic when the data are heavily censored in this paper we introduce estimation procedures for heteroskedastic censored linear regression models with a much weaker identification restriction than that required for the lcad and which are flexible enough to allow for various degrees of censoring the new estimators are shown to have desirable asymptotic properties and perform well in small scale simulation studies and can thus be considered as viable alternatives for estimating censored regression models especially for applications in which the clad fails

nonparametric estimates of regression quantiles and their local bahadur representation let x y be a random vector such that x is d dimensional y is real valued and y theta x varepsilon where x and varepsilon are independent and the alpha th quantile of varepsilon is 0 alpha is fixed such that 0 0 and set r p m 2p d where m is a nonnegative integer smaller than p let t theta denote a derivative of theta of order m it is proved that there exists a pointwise estimate hat t n of t theta based on a set of i i d observations x 1 y 1 cdots s n y n that achieves the optimal nonparametric rate of convergence n r under appropriate regularity conditions further a local bahadur type representation is shown to hold for the estimate hat t n and this is used to obtain some useful asymptotic results

energy gap for yang mills connections ii arbitrary closed riemannian manifolds abstract we prove an l d 2 energy gap result for yang mills connections on principal g bundles p over arbitrary closed riemannian smooth manifolds of dimension d 2 we apply our version of the ojasiewicz simon gradient inequality 16 19 to remove a positivity constraint on a combination of the ricci and riemannian curvatures in a previous l d 2 energy gap result due to gerhardt 23 theorem 1 2 and a previous l energy gap result due to bourguignon lawson and simons 10 theorem c 11 theorem 5 3 as well as an l 2 energy gap result due to nakajima 42 corollary 1 2 for a yang mills connection over the sphere s d but with an arbitrary riemannian metric

partial identification and inference in censored quantile regression abstract in this paper we study partial identification and inference in a linear quantile regression where the dependent variable is subject to possibly unknown dependent censoring characterized by an archimedean copula an outer set of the identified set for the regression coefficient is characterized via inequality constraints for one parameter ordered families of archimedean copulas we construct a simple confidence set by inverting an asymptotically pivotal statistic a bootstrap confidence set is also constructed sensitivity of the identified set to possible misspecification of the true copula and the finite sample performance of the boostrap confidence set are investigated numerically

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

bayesian analysis of disturbances variance in the linear regression model under asymmetric loss functions the present paper obtains a bayes estimator of the disturbance variance in a linear regression model under two asymmetric loss functions viz linex loss function and squarex loss function assuming a natural conjugate prior distribution for the parameters the expression for the bayes risk of the estimator is also derived

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

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

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

a semiparametric maximum likelihood estimator this paper presents a procedure for analyzing a model in which the parameter vector has two parts a finite dimensional component 8 and a nonparametric component a the procedure does not require parametric modeling of but assumes that the true density of the data satisfies an index restriction the idea is to construct a parametric model passing through the true model and to estimate by setting the score for the parametric model to zero the score is estimated nonparametrically and the estimator is shown to be n consistent and asymptotically normal the estimator is then shown to attain the semiparametric efficiency bound characterized in begun et al 1983 for multivariate nonlinear regression simultaneous equations partially specified regression index regression censored regression switching regression and disequilibrium models in which the error densities are unknown

censored regression quantiles abstract the object of this paper is to demonstrate how the lad estimation method for the censored regression model can be extended to more general quantiles in this paper the form of the conditional quantiles for the censored regression models is heuristically derived and discussed the resulting estimators of the regression coefficients which include the censored lad estimator as a special case are shown to be consistent and asymptotically normally distributed under appropriately translated versions of the corresponding assumptions for the former approach consistent estimation of the asymptotic covariance matrix when the error terms are i i d is also treated the paper discussed how several quantile estimators might be combined to improve efficiency when the error terms are identically distributed and how tests of homoskedasticity and symmetry of the error distribution can be constructed using particular differences of the estimated coefficients

estimation of a nonparametric censored regression model with an application to unemployment insurance spells in this paper we consider identification and estimation of a censored nonparametric location scale model we first show that in the case where the location function is strictly less than the fixed censoring point for all values in the support of the explanatory variables then the location function is not identified anywhere in contrast if the location function is greater or equal to the censoring point with positive probability then the location function is identified on the entire support including the region where the location function is below the censoring point in the latter case we propose a simple estimation procedure based on combining conditional quantile estimators for three distinct quantiles the new estimator is shown to converge at the optimal nonparametric rate with a limiting normal distribution a small scale simulation study indicates that the proposed estimation procedure performs well in finite samples we also present an empirical application to unemployment insurance duration using administrative level data from new jersey jel classification c14 c24 j64 j65

conditional empirical processes consider a sequence i xi yi i 1 of independent d 1 random vectors with common d f h text h left text x y right mathbb p left text x x y y right text left text x y right in mathbb r text d 1

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

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

estimation of censored quantile regression for panel data with fixed effects this article investigates estimation of censored quantile regression qr models with fixed effects standard available methods are not appropriate for estimation of a censored qr model with a large number of parameters or with covariates correlated with unobserved individual heterogeneity motivated by these limitations the article proposes estimators that are obtained by applying fixed effects qr to subsets of observations selected either parametrically or nonparametrically we derive the limiting distribution of the new estimators under joint limits and conduct monte carlo simulations to assess their small sample performance an empirical application of the method to study the impact of the 1964 civil rights act on the black white earnings gap is considered supplementary materials for this article are available online

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

robust bayesian analysis of a multivariate dynamic model abstract recently a bayesian approach has been widely used to infer parameters of complex models from finite sample data in business finance social and physical sciences bayesian applications in finance literature are growing due to their exposure to prior beliefs that macroeconomic variables influence the financial behavior of customers investors and firm s performance this paper employs a robust bayesian analysis model to capture a complex multi dimensional process and estimate the required parameters of interest it considers a class of prior distributions for the parameters that is a mixture of natural conjugate base priors and a contamination class of prior distributions the conditional type ii maximum likelihood posterior densities and posterior means for the coefficients vector and autoregressive parameter are derived for the coefficients vector and autoregressive parameter of interest the markov chain monte carlo mcmc method has been used for obtaining the marginal posterior densities and bayes estimators for various combinations of the parameters the usefulness of the model is demonstrated on indian financial firms balance sheets data between 1992 to 2015 to observe the sensitivity of the proposed model the result shows most of the corporate performance variables are significantly affecting the firm s profitability with the exception of interest coverage ratio

robust estimation based on grouped adjusted data in censored regression models abstract this paper considers robust estimation of censored regression models an alternative estimator to powell s lad estimator is proposed the estimation method is based on grouping consistency and asymptotical normality of the estimator are proved

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

convergence rate of empirical bayes estimation for two dimensional truncation parameters under linex loss this paper deals with the empirical bayes eb estimation for two dimensional truncation parameters under linex loss by using kernel estimation of density function we construct the eb estimation of parameters under some suitable conditions we prove that the constructed eb estimations is asymptotically optimal and we obtain its convergence rate

efficient estimation in dynamic conditional quantile models in this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data we construct an m estimator which achieves the semiparametric efficiency bound recently derived by komunjer and vuong forthcoming our efficient m estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density the estimator is new and not yet seen in the literature we illustrate its performance through a monte carlo experiment

nonparametric estimation of an additive quantile regression model this article is concerned with estimating the additive components of a nonparametric additive quantile regression model we develop an estimator that is asymptotically normally distributed with a rate of convergence in probability of n r 2r 1 when the additive components are r times continuously differentiable for some r 2 this result holds regardless of the dimension of the covariates and thus the new estimator has no curse of dimensionality in addition the estimator has an oracle property and is easily extended to a generalized additive quantile regression model with a link function the numerical performance and usefulness of the estimator are illustrated by monte carlo experiments and an empirical example

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

on average derivative quantile regression for fixed 0 1 the quantile regression function gives the th quantile x in the conditional distribution of a response variable y given the value x x of a vector of covariates it can be used to measure the effect of covariates not only in the center of a population but also in the upper and lower tails a functional that summarizes key features of the quantile specific relationship between x and y is the vector of weighted expected values of the vector of partial derivatives of the quantile function x in a nonparametric setting can be regarded as a vector of quantile specific nonparametric regression coefficients in survival analysis models e g cox s proportional hazard model proportional odds rate model accelerated failure time model and in monotone transformation models used in regression analysis gives the direction of the parameter vector in the parametric part of the model can also be used to estimate the direction of the parameter vector in semiparametric single index models popular in econometrics we show that under suitable regularity conditions the estimate of obtained by using the locally polynomial quantile estimate of chaudhuri 1991a is n 1 2 consistent and asymptotically normal with asymptotic variance equal to the variance of the influence function of the functional we discuss how the estimate of can be used for model diagnostics and in the construction of a link function estimate in general single index models

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

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

simulation and the asymptotics of optimization estimators on demontre un theoreme de limite centrale general pour des estimateurs definis par minimisation de la longueur d une fonction de critere aleatoire a valeurs vectorielles aucune hypothese de regularite suffisante n est imposee sur la fonction de critere pour que les resultats puissent etre appliques a une classe d estimlateurs de simulation assez large des analyses completes de deux estimateurs de simulation l un introduit par pakes l autre par mcfadden illustrent l application des theoremes generaux

two step estimation of semiparametric censored regression models root n consistent estimators of the regression coecients in the linear censored regression model under conditional quantile restrictions on the error terms were pro posed by powell journal of econometrics 25 1984 303 325 32 1986a 143 155 while those estimators have desirable asymptotic properties under weak regularity conditions simulation studies have shown these estimators to exhibit a small sam ple bias in the opposite direction of the least squares bias for censored data this paper introduces two step estimators for these models which minimize convex objec tive functions and are designed to overcome thisnite sample bias the paper gives regularity conditions under which the proposed two step estimators are consistent and asymptotically normal a monte carlo study compares thenite sample behavior of the proposed methods with their one step counterparts 2001 elsevier science s a all rights reserved

bayesian estimation and prediction using asymmetric loss functions abstract estimators and predictors that are optimal relative to varian s asymmetric linex loss function are derived for a number of well known models their risk functions and bayes risks are derived and compared with those of usual estimators and predictors it is shown that some usual estimators for example a scalar sample mean or a scalar least squares regression coefficient estimator are inadmissible relative to asymmetric linex loss by providing alternative estimators that dominate them uniformly in terms of risk

kernel and nearest neighbor estimation of a conditional quantile let x 1 z 1 x 2 z 2 x n z n be iid as x z and for 0 p 1 let p x denote the conditional p quantile of z given x x i e p z p x x x p kernel and near est neighbor estimators of p x are proposed in order to study the asymptotics of these estimates bahadur type representations of the sample conditional quantiles are obtained these representations are used to examine the important issue of choosing the smoothing parameter by a local approach for a fixed x based on weak convergence of these estimators the results lead to asymptotic linear models which motivate certain estimators