标题： 多元线性结构与功能误差变量模型中的新中心极限定理 显示英文标题

标题： New multivariate central limit theorems in linear structural and functional error-in-variables models

摘要： 本文同时研究了线性结构误差变量模型和函数误差变量模型（SEIVM 和 FEIVM），并在这一背景下重新审视了斜率和截距的广义最小二乘估计量和修正最小二乘估计量，以及未知测量误差方差的一些矩方法估计量。 在某些首次提出的、迄今为止最一般的条件下，针对 SEIVM 和 FEIVM 中这些估计量建立了新的联合中心极限定理（CLT）。此外，由于这些估计量最初是以学生化形式给出的，因此所得的 CLT 几乎完全基于数据，且不受误差分布未知参数及与解释变量相关的任何参数的影响。 相比之下，在迄今为止文献中的相关 CLT 中，极限正态分布的协方差矩阵通常很复杂，并依赖于多种通常未知且难以估计的参数。此外，本文中的 CLT 形式对于 SEIVM 和 FEIVM 是通用的，这扩展了之前已知的 SEIVM 和 FEIVM 之间的相互关系。 此外，尽管本文建立的 SEIVM 和 FEIVM 的 CLT 的具体方法和证明细节有所不同，但为这两个模型构建了一个统一的一般性证明方案。 显示英文摘要

摘要： This paper deals simultaneously with linear structural and functional error-in-variables models (SEIVM and FEIVM), revisiting in this context generalized and modified least squares estimators of the slope and intercept, and some methods of moments estimators of unknown variances of the measurement errors. New joint central limit theorems (CLT's) are established for these estimators in the SEIVM and FEIVM under some first time, so far the most general, respective conditions on the explanatory variables, and under the existence of four moments of the measurement errors. Moreover, due to them being in Studentized forms to begin with, the obtained CLT's are a priori nearly, or completely, data-based, and free of unknown parameters of the distribution of the errors and any parameters associated with the explanatory variables. In contrast, in related CLT's in the literature so far, the covariance matrices of the limiting normal distributions are, in general, complicated and depend on various, typically unknown parameters that are hard to estimate. In addition, the very forms of the CLT's in the present paper are universal for the SEIVM and FEIVM. This extends a previously known interplay between a SEIVM and a FEIVM. Moreover, though the particular methods and details of the proofs of the CLT's in the SEIVM and FEIVM that are established in this paper are quite different, a unified general scheme of these proofs is constructed for the two models herewith.