污染数据线性回归模型的参数估计和区间估计

Parameter Estimations and Interval Estimation in Linear Regression Model for Contaminated Data

研究线性回归模型:yi=α+βxi+iε,i=1,2,…,n,其中Eiε=0,E2iε=21σ;但y1,y2,…,yn受到另一个独立同分布随机变量序列W1,W2,…,Wn的污染,仅能观察到yi*=(1-v)yi+vwi,i=1,2,…,n,Wi与yi相互独立.文章给出了α,β,v的估计及区间估计.

The analysis of contaminated data is getting more and more attention in recent years. This paper studies linear regression model ： yi =α＋βxi ＋εi, i = 1,2, ... , n, where εi = 0, Eεi^2 = σ1^2, but y1 , y2,... , yn are contaminated by another i. i. d random variable sequenceW1 , W2, ... , Wn, is independent of yi, and only the contaminated data yi^＊ =（1-v）yi＋vwi,i=1,2, ..., n, Wi are observable, This paper gives parameter estimations and interval estimation of α, vandβ.