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摘要翻译：
本文同时讨论了线性结构和泛函变量误差模型（SEIVM和FEIVM）,在此背景下重新讨论了斜率和截距的广义和修正最小二乘估计，以及测量误差未知方差的矩估计方法。本文首次在解释变量的最一般条件下，并在测量误差存在四个矩的情况下，对SEIVM和FEIVM中的这些估计量建立了新的联合中心极限定理(CLT's)。此外，由于它们一开始是研究的形式，因此所得到的CLT几乎或完全是先验的基于数据的，没有误差分布的未知参数和与解释变量有关的任何参数。相比之下，在迄今为止的相关文献中，极限正态分布的协方差矩阵一般是复杂的，并且依赖于各种典型的难以估计的未知参数。此外，本文中的CLT的形式对于SEIVM和FEIVM是通用的。这扩展了先前已知的SEIVM和FEIVM之间的相互作用。此外，尽管本文所建立的SEIVM和FEIVM中CLT的具体证明方法和细节有很大的不同，但本文为这两个模型构造了一个统一的证明通用方案。
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英文标题：
《New multivariate central limit theorems in linear structural and
functional error-in-variables models》
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作者：
Yuliya V. Martsynyuk
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
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.
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PDF链接：
https://arxiv.org/pdf/709.0871
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