污染数据回归分析中参数的最小一乘估计
Least Absolute Deviation Estimator of Parameter in Regression Analysis for Contamination Data
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摘要: 考虑简单回归模型:y_i=x_i^\prime \beta+e_i, \quad i=1, \cdots, n,其中\mathrmE e_i=0, \mathrmE e_i^2=\sigma_1^2,假设y1, y2, …,yn受到另一独立同分布随机变量序列μ1,μ2,...,μn的污染；我们仅能观察到污染数据y_i^*=(1-\nu) y_i+\nu \mu_i, \quad 0 \leq \nu<1,v为未知的污染参数．本文用污染数据给出了β的最小一乘估计，并证明了它的渐近正态性和相合性。Abstract: Consider the simple regression model y_i=x_i^\prime \beta+e_i, i=1, \cdots, n, where \mathrmE e_i=0, \mathrmE e_i^2=\sigma_1^2 Assume that y1, y2, …,yn are contaminated by another i.i.d. random variable variable sequence μ1,μ2,...,μn and only the contaminated data y_i^*=(1-\nu) y_i+\nu \mu_i are observable, where 0≤v<1 is unknown contaminated parameter. In this paper we give LADE \widehat\beta_n of β by contamination data and establish its asymptotic normality and consistency.
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