Central limit theorem of linear regression model under right censorship

In this paper,the estimation of joint dlstribution F(y,z)of(Y,Z)and the estimation in thelinear regression model Y=b'Z+εfor complete data are extended to that of the right censored data.Theregression parameter estimates of b and the variance of ε are weighted least square estimates with randomweights. The central limit theorems of the estimators are obtained under very weak conditions and the derivedasymptotic variance has a very simple form.     

误差为线性过程时回归模型的估计问题

对一类非线性回归模型及线性模型，在误差是一个弱平稳线性过程及适当的条件下，获得了估计量的r-阶平均相合性、完全相合性和渐近正态性。     

Parameter estimation of varying coefficients structural EV model with time series

In this paper, the parameters of a p-dimensional linear structural EV (error-in-variable) model are estimated when the coefficients vary with a real variable and the model error is time series. The adjust weighted least squares (AWLS) method is used to estimate the parameters. It is shown that the estimators are weakly consistent and asymptotically normal, and the optimal convergence rate is also obtained. Simulations study are undertaken to illustrate our AWLSEs have good performance.     

On an autoregressive model with time-dependent coefficients

Summary As one of the non-stationary time series model, we consider a firstorder autoregressive model in which the autoregressive coefficient is assumed to be a function,f _t (θ), of timet. We establish several assumptions onf _t (θ), not on the terms in the Taylor expansion of log-likelihood function, and show that the estimators of unknown parameters involved inf _t (θ) have strong consistency and asymptotic normality under these assumptions when sample size tends to infinity.     

局部平稳扩散模型中时变参数的加权最小二乘估计

基于离散观测样本,利用局部线性拟合,得到了局部平稳扩散模型中时变漂移参数的加权最小二乘估计,并讨论了估计量的相合性,渐近正态性和一致收敛速度.同时,通过模拟研究说明了估计量的有效性.     

Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.     

Iterative Weighted Semiparametric Least Squares Estimation in Repeated Measurement Partially Linear Regression Models

Consider a repeated measurement partially linear regression model with an unknown vector parameter β, an unknown function g(.), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions.     

Asymptotic properties of projections with applications to stochastic regression problems

Almost sure convergence properties of least-squares estimates in stochastic regression models and an asymptotic theory of related Euclidean projections are developed herein. Applications to autoregressive processes and to dynamic input-output systems are also discussed.     

误差为线性过程时半参数模型的估计

对半参数模型Ynt=β·tni＋g（xni）＋εni,（1≤i≤n）,利用一般权函数并综合最小二乘法,定义了β,g的估计量βn,gn．在误差为线性过程时,获得了βn和gn的r阶矩相合性及gn的渐进正态性．     

局部平稳短期利率扩散模型的半参数估计

主要研究局部平稳扩散模型的半参数估计．首先,基于局部常数拟合,利用局部加权最小二乘法得到了漂移参数函数的估计量．同时,通过Kolmogorov向前方程,得到了扩散函数的估计量．然后,分别讨论了所得估计量的相合性和渐近正态性．最后,通过模拟研究说明了估计量的有效性．     

随机适应误差下线性模型参数M估计的渐近性质

在一些较弱的充分条件下,本文研究了误差为随机适应序列下,线性模型回归参数M估计的强相合性.与文献中已有结果比较,扩大了应用范围,且对矩条件也有较大改进.同时我们给出了随机适应误差下线性模型参数M估计的渐近正态性.     

Linear EV model with replicate observations on independent variables

This paper studies the linear EV model when replicate observations are made only on independent variables. We construct the estimates of regression coefficients and prove the consistency and asymptotic normality under some proper conditions. Results obtained reveal the difference between the case where the independent and dependent variables are observed repeatedly and simultaneously and the case studied in this article.     

Asymptotic normality of wavelet estimator in heteroscedastic regression model

The following heteroscedastic regression model Y_i=g(x_i) σ_ie_i(1≤i≤n)is considered,where it is assumed thatσ_i~2=f(u_i),the design points(x_i,u_i)are known and nonrandom,g and f are unknown functions.Under the unobservable disturbance e_i form martingale differences,the asymptotic normality of wavelet estimators of g with f being known or unknown function is studied.     

Estimation of partial linear error-in-response models with validation data

In this paper, an estimation theory in partial linear model is developed when there is measurement error in the response and when validation data are available. A semiparametric method with the primary data is used to define two estimators for both the regression parameter and the nonparametric part using the least squares criterion with the help of validation data. The proposed estimators of the parameter are proved to be strongly consistent and asymptotically normaal, and the estimators of the nonparametric part are also proved to be strongly consistent and weakly consistent with an optimal convergent rate. Then, the two estimators of the parameter are compared based on their empirical performances. Supported by NNSF of China (No. 10231030, No. 10241001) and a grant to the author for his excellent Ph.D. dissertation work in China.     

Fuzzy weighted scaled coefficients in semi-parametric model

In general, the regressor variables are stochastic, Duan and Li (1987, J. Econometrics, 35, 25–35), Li and Duan (1989, Ann. Statist., 17, 1009–1052) have been shown that under very general design conditions, the least squares method can still be useful in estimating the scaled regression coefficients of the semi-parametric model Y _i =Q ₁(+X _i ; _i , i+ 1,2,...,n. Here is a constant, is a 1×p row vector, X _i is a p×1 column vector of explanatory variables, _i is an unobserved random error and Q ₁ is an arbitrary unknown function. When the data set (X _i , Y _i ),i=1, 2, ..., n, contains one or several outliers, the least squares method can not provide a consistent estimator of the scaled coefficients . Therefore, we suggest the fuzzy weighted least squares method to estimate the scaled coefficients for the data set with one or several outliers. It will be shown that the proposed fuzzy weighted least squares estimators are % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaakaaabaGaamOBaaWcbeaaaaa!3D3C!\[\sqrt n \] and asymptotically normal under very general design condition. Consistent measurement of the precision for the estimator is also given. Moreover, a limited Monte Carlo simulation and an example are used to study the practical performance of the procedures.This research partially supported by the National Science Council, R.O.C.     

Efficient robust estimation of time-series regression models

The paper studies a new class of robust regression estimators based on the two-step least weighted squares (2S-LWS) estimator which employs data-adaptive weights determined from the empirical distribution or quantile functions of regression residuals obtained from an initial robust fit. Just like many existing two-step robust methods, the proposed 2S-LWS estimator preserves robust properties of the initial robust estimate. However, contrary to the existing methods, the first-order asymptotic behavior of 2S-LWS is fully independent of the initial estimate under mild conditions. We propose data-adaptive weighting schemes that perform well both in the cross-section and time-series data and prove the asymptotic normality and efficiency of the resulting procedure. A simulation study documents these theoretical properties in finite samples.     

Stochastic optimization with averaging of trajectories

A recursive stochastic optimization procedure under dependent disturbances is studied. It is based on the Polyak-Ruppert algorithm with trajectory averaging. Almost sure convergence of the algorithm is proved as well as asymptotic normality of the delivered estimates. It is shown that the presented algorithm attains the highest possible asymptotic convergence rate for stochastic approximation algorithms     

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.     

Large-Sample Theory for Generalized Linear Models with Non-natural Link and Random Variates

For generalized linear models （GLM）, in the ease that the regressors are stochastie and have different distributions and the observations of the responses may have different dimcnsionality, the asyinptotic theory of the maximum likelihood estimate （MLE） of the parameters are studied under the assumption of a non-natural link funetion,     

基于最小二乘近似的模型平均方法

本文提出基于最小二乘近似的模型平均方法.该方法可用于线性模型、广义线性模型和分位数回归等各种常用模型.特别地,经典的Mallows模型平均方法是该方法的特例.现存的模型平均文献中,渐近分布的证明一般需要局部误设定假设,所得的极限分布的形式也比较复杂.本文将在不使用局部误设定假设的情形下证明该方法的渐近正态性.另外,本文...