�̶�ЧӦ������ݲ�������ģ�͵ļ�Ȩ����LSDV����

This paper concerns with the estimation of a fixed effects panel data partially linear regression model with the idiosyncratic errors being an autoregressive process. For fixed effects short time series panel data, the commonly used autoregressive error structure fitting method will not result in a consistent estimator of the autoregressive coefficients. Here we propose an alternative estimation and show that the resulting estimator of the autoregressive coefficients is consistent and this method is workable for any order autoregressive error structure. Moreover, combining the B-spline approximation, profile least squares dummy variable (PLSDV) technique and consistently estimated the autoregressive error structure, we develop a weighted PLSDV estimator for the parametric component and a weighted B-spline series (BS) estimator for the nonparametric component. The weighted PLSDV estimator is shown to be asymptotically normal and more asymptotically efficient than the one which ignores the error autoregressive structure. In addition, this paper derives the asymptotic bias of the weighted BS estimator and establish its asymptotic normality as well. Simulation studies and an example of application are conducted to illustrate the finite sample performance of the proposed procedures.     

Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors

We consider a panel data semiparametric partially linear regression model with an unknown parameter vector for the linear parametric component, an unknown nonparametric function for the nonlinear component, and a one-way error component structure which allows unequal error variances (referred to as heteroscedasticity). We develop procedures to detect heteroscedasticity and one-way error component structure, and propose a weighted semiparametric least squares estimator (WSLSE) of the parametric component in the presence of heteroscedasticity and/or one-way error component structure. This WSLSE is asymptotically more efficient than the usual semiparametric least squares estimator considered in the literature. The asymptotic properties of the WSLSE are derived. The nonparametric component of the model is estimated by the local polynomial method. Some simulations are conducted to demonstrate the finite sample performances of the proposed testing and estimation procedures. An example of application on a set of panel data of medical expenditures in Australia is also illustrated.     

Iterative weighted partial spline least squares estimation in semiparametric modeling of longitudinal data

In this paper we consider the estimating problem of a semiparametric regression modelling whenthe data are longitudinal.An iterative weighted partial spline least squares estimator(IWPSLSE)for the para-metric component is proposed which is more efficient than the weighted partial spline least squares estimator(WPSLSE)with weights constructed by using the within-group partial spline least squares residuals in the sense     

Penalized maximum likelihood estimation of a stochastic multivariate regression model

We study the large-sample properties of the penalized maximum likelihood estimator of a multivariate stochastic regression model with contemporaneously correlated data. The penalty is in terms of the square norm of some (vector) linear function of the regression coefficients. The model subsumes the so-called common transfer function model useful for extracting common signals in a panel of short time series. We show that, under mild regularity conditions, the penalized maximum likelihood estimator is consistent and asymptotically normal. The asymptotic bias of the regression coefficient estimator is also derived.     

变系数部分线性模型的加权随机约束s-K估计

研究随机约束条件下半参数变系数部分线性模型的参数估计问题,当回归模型线性部分变量存在多重共线性时,基于Profile最小二乘方法、s-K估计和加权混合估计构造参数向量的加权随机约束s-K估计,并在均方误差矩阵准则下给出新估计量优于s-K估计和加权混合估计的充要条件,最后通过蒙特卡洛数值模拟验证所提出估计量的有限样本性质.     

Detection of outliers in weighted least squares regression

In multiple linear regression model, we have presupposed assumptions (independence, normality, variance homogeneity and so on) on error term. When case weights are given because of variance heterogeneity, we can estimate efficiently regression parameter using weighted least squares estimator. Unfortunately, this estimator is sensitive to outliers like ordinary least squares estimator. Thus, in this paper, we proposed some statistics for detection of outliers in weighted least squares regression.     

˫�������ɷֵĿռ����ģ�͵IJ�������

??In this paper, we construct a generalized spatial panel data model with two-way error components where the spatial correlation also exist in the individual effects. Based on the methods of the generalized moment estimate and the two-step least square estimate, we look for the best instrumental variable, fit generalized moments and the weighted matrix to discuss the estimator of the parameters, and prove the consistent of the estimators. Monte Carlo experiments show that the weighted generalized moment estimators are better than the unweighted generalized moment estimators, and the estimate effect of feasible generalized two stages least squares estimators is good.     

加权平衡损失函数下回归系数的最佳线性无偏估计

这篇文章我们研究了回归系数的最佳线性无偏估计. 在加权平衡损失函数下, 我们得到了回归系数的最佳线性无偏估计. 同时提出了度量最佳线性无偏估计和最小二乘估计的相对效率. 并且我们给出了它们的上下界.     

左截断相依数据下条件分位数的双核局部线性估计

本文在左截断相依数据下,利用局部线性估计的方法,先提出了条件分布函数的双核估计;然后利用该估计导出了条件分位数的双核局部线性估计,并建立了这些估计的渐近正态性结果;最后,通过模拟显示该估计在偏移和边界点调节上要比一般的核估计更好.     

Some properties of projectors associated with the WLSE under a general linear model

Projectors associated with a particular estimator in a general linear model play an important role in characterizing statistical properties of the estimator. A variety of new properties were derived on projectors associated with the weighted least-squares estimator (WLSE). These properties include maximal and minimal possible ranks, rank invariance, uniqueness, idempotency, and other equalities involving the projectors. Applications of these properties were also suggested. Proofs of the main theorems demonstrate how to use the matrix rank method for deriving various equalities involving the projectors under the general linear model.     

复杂设计下类均值复制与类加权均值复制的比较（英文）

复制数据是处理抽样调查中数据项目缺失的一种常用方法。在两种常见模型及复杂抽样设计下，本文对处理数据项目缺失的类均值复制和类加权均值复制方法进行了对比。     

Nonparametric estimation of conditional medians for linear and related processes

We consider nonparametric estimation of conditional medians for time series data. The time series data are generated from two mutually independent linear processes. The linear processes may show long-range dependence. The estimator of the conditional medians is based on minimizing the locally weighted sum of absolute deviations for local linear regression. We present the asymptotic distribution of the estimator. The rate of convergence is independent of regressors in our setting. The result of a simulation study is also given.     

Local Weighted Composite Quantile Estimating for Varying Coefficient Models

A generalization of classical linear models is varying coefficient models, which offer a flexible approach to modeling nonlinearity between covariates. A method of local weighted composite quantile regression is suggested to estimate the coefficient functions. The local Bahadur representation of the local estimator is derived and the asymptotic normality of the resulting estimator is established. Comparing to the local least squares estimator, the asymptotic relative efficiency is examined for the local weighted composite quantile estimator. Both theoretical analysis and numerical simulations reveal that the local weighted composite quantile estimator can obtain more efficient than the local least squares estimator for various non-normal errors. In the normal error case, the local weighted composite quantile estimator is almost as efficient as the local least squares estimator. Monte Carlo results are consistent with our theoretical findings. An empirical application demonstrates the potential of the proposed method.     

An embedded estimating equation for the additive risk model with biased-sampling data

This paper presents a novel class of semiparametric estimating functions for the additive model with right-censored data that are obtained from general biased-sampling. The new estimator can be obtained using a weighted estimating equation for the covariate coeffcients, by embedding the biased-sampling data into left-truncated and right-censored data. The asymptotic properties (consistency and asymptotic normality) of the proposed estimator are derived via the modern empirical processes theory. Based on the cumulative residual processes, we also propose graphical and numerical methods to assess the adequacy of the additive risk model. The good finite-sample performance of the proposed estimator is demonstrated by simulation studies and two applications of real datasets.     

Asymptotic distribution of the weighted least squares estimator

This paper derives the asymptotic distribution of the weighted least squares estimator (WLSE) in a heteroscedastic linear regression model. A consistent estimator of the asymptotic covariance matrix of the WLSE is also obtained. The results are obtained under weak conditions on the design matrix and some moment conditions on the error distributions. It is shown that most of the error distributions encountered in practice satisfy these moment conditions. Some examples of the asymptotic covariance matrices are also given.     

�������ݾ�ֵ��Э����������Ч�Ƚ�����

In this article, we develop efficient robust method for estimation of mean and covariance simultaneously for longitudinal data in regression model. Based on Cholesky decomposition for the covariance matrix and rewriting the regression model, we propose a weighted least square estimator, in which the weights are estimated under generalized empirical likelihood framework. The proposed estimator obtains high efficiency from the close connection to empirical likelihood method, and achieves robustness by bounding the weighted sum of squared residuals. Simulation study shows that, compared to existing robust estimation methods for longitudinal data, the proposed estimator has relatively high efficiency and comparable robustness. In the end, the proposed method is used to analyse a real data set.     

Censored multiple regression by the method of average derivatives

This paper proposes a technique [termed censored average derivative estimation (CADE)] for studying estimation of the unknown regression function in nonparametric censored regression models with randomly censored samples. The CADE procedure involves three stages: firstly-transform the censored data into synthetic data or pseudo-responses using the inverse probability censoring weighted (IPCW) technique, secondly estimate the average derivatives of the regression function, and finally approximate the unknown regression function by an estimator of univariate regression using techniques for one-dimensional nonparametric censored regression. The CADE provides an easily implemented methodology for modelling the association between the response and a set of predictor variables when data are randomly censored. It also provides a technique for “dimension reduction” in nonparametric censored regression models. The average derivative estimator is shown to be root-n consistent and asymptotically normal. The estimator of the unknown regression function is a local linear kernel regression estimator and is shown to converge at the optimal one-dimensional nonparametric rate. Monte Carlo experiments show that the proposed estimators work quite well.     

A weighted Wilcoxon estimate for the covariate-specific ROC curve

The covariate-specific receiver operating characteristic (ROC) curve is an important tool for evaluating the classification accuracy of a diagnostic test when it is associated with certain covariates. In this paper, a weighted Wilcoxon estimator is constructed for estimating this curve under the framework of location-scale model for the test result. The asymptotic normality is established, both for the regression parameter estimator and the estimator for the covariate-specific ROC curve at a fixed false positive point. Simulation results show that the Wilcoxon estimator compares favorably to its main competitors in terms of the standard error, especially when outliers exist in the covariates. As an illustration, the new procedure is applied to the dementia data from the national Alzheimer’s coordinating center.     

Two step estimators of the minimum distance type for parameters of the ARMA(1,1) model

New minimum distance estimators are constructed with the help of a preliminary estimator. The asymptotic normality of the constructed estimator is proved with use of a uniform linear expansion of a randomly weighted residual empirical process in a non-standard neighborhood of the true parameter value. Also the question on asymptotic efficiency of the constructed estimator is discussed.     

响应变量删失时函数型部分线性分位数回归模型的估计

最近几年,函数型数据分析的理论和应用飞速发展.在许多实际应用里,响应变量往往存在随机右删失的情况.考虑利用函数型部分线性分位数回归模型来刻画函数型和标量预测量与右删失响应变量之间的关系.基于函数型主成分基函数来逼近未知的斜率函数,通过极小化逆概率加权分位数损失函数得到未知系数的估计量.文章的估计方法容易通过加权分位数回归程序实现.在一定的假设条件下,给出了有限维参数估计量的渐近正态性与斜率函数估计量的收敛速度.最后,通过模拟计算与应用实例证明了所提方法的有效性.