关于二值回归模型的两点注记

本文对二值回归模型中自变量误差的处理作了两种推广。相合Ｍ－估计的渐近正态性，最优Ｍ－方程及求解并得到最优解的计算方法，都得到相应的推广。

Two Notes On Binary Regression Models

This paper makes a discussion for errors in variables in binary repression models, in which the response Y takes the value 0 or 1 only. Firstly, the conditional probability P(Y= 1 |X=x) is assumed to be of the form G(a0+a1x+......+akxk),Whete x is the measurement of the factor, a= (a0,a1,......,ak)' is the vector of the unknown parameter being estimated and g(u)= (1 + ek)-1. The measurement x is assumed to be contaminated when the value of x is out of Certain limit. Secondly,the conditional conditional probability P(Y=1|X1=x1......,Xk=xk) is assumed to be of the form G(a0+a1x1...... +akxk), where x1, ......,xkare the measurement of the factors and x1, ......xk are assumed to be contaminated when the value of x12+......sk2 is out of certain limit. The consistenal M-estimation being asymptotically normal,the optimal M-equation and a computation method to solve the M-equation as well as to get the optimal solution,which had been given in 1] that coincides with the first form in this paper where k=1,are extended to the first form and the second form in this paper.