半变系数模型的Back-Fitting估计

针对半变系数回归模型给出了一种后向拟合方法,该方法可得到模型中常值系数估计量的精确表达式;同时给出了实验设计方法和数值模拟结果,用于验证所提出的估计方法对估计常值系数具有满意的精度和稳定性.     

半参数空间变系数回归模型的Back-Fitting估计

针对半参数空间变系数回归模型给出了一种估计方法-后向拟合估计,该方法可得到模型中常值系数估计量的精确解析表达式,广泛的数值模拟表明所提出的估计方法对估计常值系数具有满意的精度和稳定性,最后,利用该方法分析了一个实际的例子.     

半变系数模型改进的轮廓最小二乘估计

针对半变系数模型,在局部线性拟合轮廓最小二乘估计方法的基础上将关于变系数函数的局部线性拟合改进为局部非线性拟合,得到半变系数模型改进的轮廓最小二乘估计,进一步讨论了常值系数的渐进正态性.     

部分线性变系数模型Backfitting估计的渐近性质

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类应用广泛的数据分析模型.利用Backfitting方法拟合这类特殊的可加模型,可得到模型中常值系数估计量的精确解析表达式,该估计量被证明是n~(1/2)相合的.最后通过数值模拟考察了所提估计方法的有效性.     

强相依数据的函数系数部分线性模型的估计

本文讨论在数据是强相依的情况下函数系数部分线性模型的估计．首先,采用局部线性方法,给出该模型函数项函数的估计;然后,使用两阶段方法给出系数函数的估计．并且讨论了函数项函数估计的渐近正态性,以及系数函数估计的弱相合性和渐近正态性.模拟研究显示,这些估计是较为理想的．     

部分函数线性变系数模型的样条估计及其应用

本文针对Tecator数据介绍一种新的模型一部分函数线性变系数模型,并基于样条估计方法得到了模型中未知系数函数的估计,同时在适当的条件下给出了系数函数估计及模型均方预测误差的收敛速度。通过数值模拟说明本文所提估计方法的有效性。最后基于该模型对Tecator数据进行了统计分析。     

部分线性变系数模型的一种新的轮廓(Profile)最小二乘估计

作为部分线性模型和变系数模型的推广,部分线性变系数模型以其良好的适应性和稳健性受到了广泛的关注。本文基于函数的局部线性拟合,给出部分线性变系数模型的另一种轮廓(profile)最小二乘估计的方法,并从理论上证实了所得估计量具有良好的渐近性质,最后给出了估计方法的实例分析。     

误差相关的半变系数模型的估计

本文在误差相关的情况下, 研究半变系数模型的估计, 通过改进PLS估计, 给出了函数系数和常数系数的估计, 证明了估计的渐近正态性; 最后, 模拟研究说明了所提方法的有效性.     

部分线性变系数模型中误差方差的估计

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类在建模中应用非常广泛的模型.本文基于Profile最小二乘方法给出了模型中误差方差的估计并证明了该估计的渐近正态性.最后通过数值模拟验证了我们所提估计方法的有效性.     

半变系数模型约束PLS估计的渐近正态性

变系数模型已获得了广泛的应用,半变系数模型是变系数模型的有效推广,本文给出半变系数模型在线性约束条件下的PLS估计,并证明了常系数和函数系数估计的渐近正态性.     

SIMEX Estimation for Composite Quantile Regression Model with Measurement Error

Composite quantile regression model with measurement error is considered. The SIMEX estimators of the unknown regression coefficients are proposed based on the composite quantile regression. The proposed estimators not only eliminate the bias caused by measurement error, but also retain the advantages of the composite quantile regression estimation. The asymptotic properties of the SIMEX estimation are proved under some regular conditions. The finite sample properties of the proposed method are studied by a simulation study, and a real example is analyzed.     

���������ĸ��Ϸ�λ���ع��SIMEX����

??Composite quantile regression model with measurement error is considered. The SIMEX estimators of the unknown regression coefficients are proposed based on the composite quantile regression. The proposed estimators not only eliminate the bias caused by measurement error, but also retain the advantages of the composite quantile regression estimation. The asymptotic properties of the SIMEX estimation are proved under some regular conditions. The finite sample properties of the proposed method are studied by a simulation study, and a real example is analyzed.     

Interquantile Shrinkage in Regression Models

Conventional analysis using quantile regression typically focuses on fitting the regression model at different quantiles separately. However, in situations where the quantile coefficients share some common feature, joint modeling of multiple quantiles to accommodate the commonality often leads to more efficient estimation. One example of common features is that a predictor may have a constant effect over one region of quantile levels but varying effects in other regions. To automatically perform estimation and detection of the interquantile commonality, we develop two penalization methods. When the quantile slope coefficients indeed do not change across quantile levels, the proposed methods will shrink the slopes toward constant and thus improve the estimation efficiency. We establish the oracle properties of the two proposed penalization methods. Through numerical investigations, we demonstrate that the proposed methods lead to estimations with competitive or higher efficiency than the standard quantile regression estimation in finite samples. Supplementary materials for the article are available online.     

Minimax multivariate empirical Bayes estimators under multicollinearity

In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage functions, that is, scalar, componentwise and matricial shrinkage. These proposed estimators are proved to be uniformly better than the least squares estimator, that is, minimax in terms of risk under the Strawderman's loss function. Through simulation and empirical studies, they are also shown to be useful in the multicollinearity cases.     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

Comparisons among some estimators in misspecified linear models with multicollinearity

In this paper we deal with comparisons among several estimators available in situations of multicollinearity (e.g., the r-k class estimator proposed by Baye and Parker, the ordinary ridge regression (ORR) estimator, the principal components regression (PCR) estimator and also the ordinary least squares (OLS) estimator) for a misspecified linear model where misspecification is due to omission of some relevant explanatory variables. These comparisons are made in terms of the mean square error (mse) of the estimators of regression coefficients as well as of the predictor of the conditional mean of the dependent variable. It is found that under the same conditions as in the true model, the superiority of the r-k class estimator over the ORR, PCR and OLS estimators and those of the ORR and PCR estimators over the OLS estimator remain unchanged in the misspecified model. Only in the case of comparison between the ORR and PCR estimators, no definite conclusion regarding the mse dominance of one over the other in the misspecified model can be drawn.     

Multivariate Locally Weighted Polynomial Fitting and Partial Derivative Estimation

Nonparametric regression estimator based on locally weighted least squares fitting has been studied by Fan and Ruppert and Wand. The latter paper also studies, in the univariate case, nonparametric derivative estimators given by a locally weighted polynomial fitting. Compared with traditional kernel estimators, these estimators are often of simpler form and possess some better properties. In this paper, we develop current work on locally weighted regression and generalize locally weighted polynomial fitting to the estimation of partial derivatives in a multivariate regression context. Specifically, for both the regression and partial derivative estimators we prove joint asymptotic normality and derive explicit asymptotic expansions for their conditional bias and conditional convariance matrix (given observations of predictor variables) in each of the two important cases of local linear fit and local quadratic fit.     

Double Shrinkage Estimation of Common Coefficients in Two Regression Equations with Heteroscedasticity

The problem of estimating the common regression coefficients is addressed in this paper for two regression equations with possibly different error variances. The feasible generalized least squares (FGLS) estimators have been believed to be admissible within the class of unbiased estimators. It is, nevertheless, established that the FGLS estimators are inadmissible in light of minimizing the covariance matrices if the dimension of the common regression coefficients is greater than or equal to three. Double shrinkage unbiased estimators are proposed as possible candidates of improved procedures.