关于两类污染数据回归分析的参数估计

PARAMETER ESTIMATION IN REGRESSION ANALYSIS FOR TWO KINDS OF CONTAMINATION DATA

研究简单回归模型: y_i=α+βx_j+ε_j,j=1,2,…,n,其中Eε_j=0,Eε_j^2=σ_1~2;但y_1,y_2,…y_n受到另一独立同分布随机变量序列t_1,t_2,…,/t_n两种不同方式的污染,t_j与y_j独立。本文给出了两种污染方式下的α、β和污染参数的估计。

This paper studies the simple regression model y_j=α+βx_j+ε_j, j=1,2,…,n,where Eε_j=0,Eε_j^2=σ_1~2. But y_1, y_2, …, y_n are contaminated by another i. i. d. random vari-able sequence t_1,t_2, …, t_n in two different ways. {t_j} is independent of {y_j}. This papergives the estimations of α,β and contamination parameter respectively.