Efficient estimation of a varying-coefficient partially linear binary regression model

This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.     

Efficient estimation for semiparametric varying- coefficient partially linear regression models with current status data

This article considers a semiparametric varying-coefficient partially linear regression model with current status data. The semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are conducted to examine the small-sample properties of the proposed estimates and a real dataset is used to illustrate our approach.     

Asymptotically optimal estimation in a linear-fractional regression problem with random errors in coefficients

Considering the linear-fractional regression problem with errors in independent variables, we construct and study asymptotically optimal estimators for unknown parameters in the case of violation of the classical regression assumptions (the variances of the observations are different and depend on the unknown parameters).     

Ⅱ型区间删失数据下广义部分线性模型的筛极大似然估计(英文)

This article concerded with a semiparametric generalized partial linear model （GPLM） with the type Ⅱ censored data. A sieve maximum likelihood estimator （MLE） is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.     

On optimality of regular projective estimators for semimartingale models,part ii: asymptotically linear estimators

In this paper we consider estimators that (asymptotically) admit a so called linear representation. Using a parametrization of the model, that has been defined in a previous paper [1], and a certain notion of smoothness of the parametrization, it is possible to define a concept of optimality for these estimators and to characterize the optimal estimators. In contrast with the situation in [1], only the compensator is fully parametrized by the parameter we want to estimate. Embedding the problem under consideration in the previously developed framework then requires the introduction of several nuisance parameters, that are needed to describe certain stochastic integrals with respect to the compensator of the jump measure     

非零截距线性和非线性回归模型的T-型稳健估计算法

首先给出非零截距线性模型T-型估计的模型与EM算法,其次给出非线性回归模型参数的T-型估计,利用泰勒级数对模型线性化,得到参数估计的迭代算法,最后用数值模拟实验验证了该算法的正确性和证实了T-型估计的稳健性.     

Efficient Quantile Estimation for Functional-Coefficient Partially Linear Regression Models

The quantile estimation methods are proposed for functional-coefficient partially linear regression (FCPLR) model by combining nonparametric and functional-coefficient regression (FCR) model. The local linear scheme and the integrated method are used to obtain local quantile estimators of all unknown functions in the FCPLR model. These resulting estimators are asymptotically normal, but each of them has big variance. To reduce variances of these quantile estimators, the one-step backfitting technique is used to obtain the efficient quantile estimators of all unknown functions, and their asymptotic normalities are derived. Two simulated examples are carried out to illustrate the proposed estimation methodology.     

秩亏线性模型中的一个新的线性有偏估计类

本文基于最优线性最小偏差估计的谱分解,定义了秩亏线性模型未知参数的一个新的线性有偏估计类,并讨论了它的许多重要性质,通过选取偏参数的适当形式,构造了许多很有意义的线性有偏估计,最后,给出了一个算例。     

因变量缺失下线性变量含误差模型的估计

主要考虑线性模型在自变量测量含误差以及因变量缺失情况下的估计问题.对于模型中的回归系数,我们基于最小二乘方法提出了两类估计,其中一类估计只由完整观测数据构成,而另外一类估计利用的则是利用简单插补方法构造的完整数据.证明了这两类估计是渐近正态性的.     

A third order optimum property of the ML estimator in a linear functional relationship model and simultaneous equation system in econometrics

Summary The maximum likelihood (ML) estimator and its modification in the linear functional relationship model with incidental parameters are shown to be third-order asymptotically efficient among a class of almost median-unbiased and almost mean-unbiased estimators, respectively, in the large sample sense. This means that the limited information maximum likelihood (LIML) estimator in the simultaneous equation system is third-order asymptotically efficient when the number of excluded exogenous variables in a particular structural equation is growing along with the sample size. It implies that the LIML estimator has an optimum property when the system of structural equations is large. The research was partly supported by National Science Foundation Grant SES 79-13976 at the Institute for Mathematical Studies in the Social Sciences, Stanford University and Grant-in-Aid 60301081 of the Ministry of Education, Science and Culture at the Faculty of Economics, University of Tokyo. This paper was originally written as a part of the author's Ph.D. dissertation submitted to Stanford University in August, 1981. Some details of the paper were deleted at the suggestion of the associate editor of this journal.     

The 3/2th and 2nd order asymptotic efficiency of maximum probability estimators in non-regular cases

In this paper we consider the estimation problem on independent and identically distributed observations from a location parameter family generated by a density which is positive and symmetric on a finite interval, with a jump and a nonnegative right differential coefficient at the left endpoit. It is shown that the maximum probability estimator (MPE) is 3/2th order two-sided asymptotically efficient at a point in the sense that it has the most concentration probability around the true parameter at the point in the class of 3/2th order asymptotically median unbiased (AMU) estimators only when the right differential coefficient vanishes at the left endpoint. The second order upper bound for the concentration probability of second order AMU estimators is also given. Further, it is shown that the MPE is second order two-sided asymptotically efficient at a point in the above case only.Research supported by University of Tsukuba Project Research.     

ESTIMATORS AND SOME BEHAVIORS FOR A PARTIALLY LINEAR MODEL WITH CENSORED DATA

1991MRSubjectClassification62G05,62E20,62J991IntroductionInrecelltyearstherehasbeedagreatdealofinterestilltheallalysisofpal.tiallylilleal*model.Speckman[']proposedaluethodofkernelsmoothingandthepartialregressionestinlator.ChenandShiau[2]showedthatatwo-stagesplinesmoothingmethodanddiscussedthelarge-samplebehavioroftwoefficientestimatorsforthepararl--letriccorxlponentofapartiallylineal.model.Inthispaper,weconsidertheestimationofpartiallylinearlliodelwith,f..sorilig.Anappealingnonparallletric…     

The Minimax Estimator of Stochastic Regression Coefficients and Parameters in the Class of All Estimators

In this paper, the authors address the problem of the minimax estimator of linear combinations of stochastic regression coefficients and parameters in the general normal linear model with random effects. Under a quadratic loss function, the minimax property of linear estimators is investigated. In the class of all estimators, the minimax estimator of estimable functions, which is unique with probability 1, is obtained under a multivariate normal distribution.     

Efficient and fast spline-backfitted kernel smoothing of additive models

A great deal of effort has been devoted to the inference of additive model in the last decade. Among existing procedures, the kernel type are too costly to implement for high dimensions or large sample sizes, while the spline type provide no asymptotic distribution or uniform convergence. We propose a one step backfitting estimator of the component function in an additive regression model, using spline estimators in the first stage followed by kernel/local linear estimators. Under weak conditions, the proposed estimator’s pointwise distribution is asymptotically equivalent to an univariate kernel/local linear estimator, hence the dimension is effectively reduced to one at any point. This dimension reduction holds uniformly over an interval under assumptions of normal errors. Monte Carlo evidence supports the asymptotic results for dimensions ranging from low to very high, and sample sizes ranging from moderate to large. The proposed confidence band is applied to the Boston housing data for linearity diagnosis. Supported in part by NSF awards DMS 0405330, 0706518, BCS 0308420 and SES 0127722.     

正态-逆Wishart先验下多元线性模型中经验Bayes估计的优良性

在正态-逆Wishart先验下研究了多元线性模型中参数的经验Bayes估计及其优良性问题.当先验分布中含有未知参数时,构造了回归系数矩阵和误差方差矩阵的经验Bayes估计,并在Bayes均方误差(简称BMSE)准则和Bayes均方误差阵(简称BMSEM)准则下,证明了经验Bayes估计优于最小二乘估计.最后,进行了Monte Carlo模拟研究,进一步验证了理论结果.     

ADMISSIBILITY OF LINEAR ESTIMATORS IN A GROWTH CURVE MODEL SUBJECT TO AN INCOMPLETE ELLIPSOIDAL RESTRICTION

This article considers the admissibility of the linear estimators for the regression coefficients in the growth curve model subject to an incomplete ellipsoidal restriction. The necessary and sufficient conditions for linear estimators to be admissible in classes of the homogeneous and non-homogeneous linear estimators, respectively, are obtained under the quadratic loss function. They are generalizations of some existing results in literature.     

Minimum Disparity Estimation in Linear Regression Models: Distribution and Efficiency

This paper deals with the minimum disparity estimation in linear regression models. The estimators are defined as statistical quantities which minimize the blended weight Hellinger distance between a weighted kernel density estimator of errors and a smoothed model density of errors. It is shown that the estimators of the regression parameters are asymptotic normally distributed and efficient at the model if the weights of the density estimators are appropriately chosen.     

Asymptotically optimal estimation in a linear regression problem with random errors in coefficients

We consider the problem of estimating an unknown one-dimensional parameter in the linear regression problem in the case when the independent variables (called coefficients in the article) are measured with errors, and the variances of the principal observations can depend on the main parameter. We study the behavior of two-step estimators, previously introduced by the authors, which are asymptotically optimal in the case when the independent variables are measured without errors. Under sufficiently general assumptions we find necessary and sufficient conditions for the asymptotic normality and asymptotic optimality of these estimators in the new setup.     

A Class of Linear Biased Estimators of Regression ParameterMatrix in the Growth Curve Model

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Randomly censored partially linear single-index models

This paper proposes a method for estimation of a class of partially linear single-index models with randomly censored samples. The method provides a flexible way for modelling the association between a response and a set of predictor variables when the response variable is randomly censored. It presents a technique for “dimension reduction” in semiparametric censored regression models and generalizes the existing accelerated failure-time models for survival analysis. The estimation procedure involves three stages: first, transform the censored data into synthetic data or pseudo-responses unbiasedly; second, obtain quasi-likelihood estimates of the regression coefficients in both linear and single-index components by an iteratively algorithm; finally, estimate the unknown nonparametric regression function using techniques for univariate censored nonparametric regression. The estimators for the regression coefficients are shown to be jointly root-n consistent and asymptotically normal. In addition, the estimator for the unknown regression function is a local linear kernel regression estimator and can be estimated with the same efficiency as all the parameters are known. Monte Carlo simulations are conducted to illustrate the proposed methodology.