污染数据回归分析中估计的强相合性

Strong Consistency of Estimates in Regression Analysis for Contamination Data

摘要: 考虑简单回归模型（Ⅰ）y_i＝α＋x_iβ＋ε_i，i＝1，2，…，n,与半参数回归模型（Ⅱ）y_i＝x_iβ＋g（t_i）+ε_i，i＝1，2，…，n其中 Eε_i＝0， Eε_i²＝σ₁²,假定y₁, y₂,…, y_n受到另一独立同分布随机变量序列μ₁，μ₂，…，μ_n的污染，且仅能观察到污染数据，μ_i与｛y_i｝独立。对文1，2中给出的α，β，g（·）及污染参数v的估计，本文在适当的条件下，证明了它们的强相合性。

Abstract: Consider the simple regraseion model （Ⅰ）y_i＝α＋x_iβ＋ε_i，i＝1，2，…，n, and the semipara-metric regression model （Ⅱ）y_i＝x_iβ＋g（t_i）+ε_i，i＝1，2，…，n. Where Eε_i＝0， Eε_i²＝σ₁². Assume that y₁, y₂,…, y_n are contammated by another i.i.d. random variable sequence μ₁，μ₂，…，μ_n, and only the contaminated data are observable, where μ_i is independent of y_i . For the estimates of α，β，g（·） and contammation parameter v given in 1 and 2, we establish their strong consistency under suitable conditions