摘要翻译：
研究了线性结构变量误差模型中斜率和截距的修正最小二乘估计。假定测量误差存在四个矩，且解释变量在正态律的吸引域内，对这些估计量建立了新的边际中心极限定理。后一个解释变量的条件是第一次使用的，而且是目前为止在这种情况下最普遍的。对于我们的CLT来说，它也是最优的，或者几乎是最优的。此外，由于所得到的CLT一开始是研究的和自归一化的形式，它们几乎或完全是先验的基于数据的，并且没有误差和解释变量联合分布的未知参数。因此，它们导致了斜率和截距的各种容易获得或容易导出的大样本近似置信区间(CI's)。与此相反，在迄今为止的相关文献中，极限正态分布的方差通常是复杂的，并依赖于各种通常未知的误差矩和解释变量。因此，与本文不同的是，文献中关于斜率和截距的相应CI仅在一些附加的模型假设下可用。
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英文标题：
《Central limit theorems in linear structural error-in-variables models
  with explanatory variables in the domain of attraction of the normal law》
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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：
  Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these estimators, assuming the existence of four moments for the measurement errors and that the explanatory variables are in the domain of attraction of the normal law. The latter condition for the explanatory variables is used the first time, and is so far the most general in this context. It is also optimal, or nearly optimal, for our CLT's. Moreover, due to the obtained CLT's being in Studentized and self-normalized forms to begin with, they are a priori nearly, or completely, data-based, and free of unknown parameters of the joint distribution of the error and explanatory variables. Consequently, they lead to a variety of readily available, or easily derivable, large-sample approximate confidence intervals (CI's) for the slope and intercept. In contrast, in related CLT's in the literature so far, the variances of the limiting normal distributions, in general, are complicated and depend on various, typically unknown, moments of the error and explanatory variables. Thus, the corresponding CI's for the slope and intercept in the literature, unlike those of the present paper, are available only under some additional model assumptions.
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PDF链接：
https://arxiv.org/pdf/706.0826