| 郑忠国.二值回归模型中自变量误差的处理[J].数学研究及应用,1987,7(2):305~310 |
| 二值回归模型中自变量误差的处理 |
| Errors in variables in binary regression models |
| 投稿时间：1983-05-05 |
| DOI：10.3770/j.issn:1000-341X.1987.02.022 |
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| In this paper the binary regression model, in which the response Y is binary, i.e. Y takes the value 0 or 1 only, is considered. The conditional probability P{Y=1|X=x} is assumed to be of the form G(a0+a1x), where x is the measurement of the factor, a= (a0,a1)′ is the vector of the unknown parameter being estimated and G(a) = (1+ea)-1. The measurement x is assu-med to be contaminated when the value of x is out of certain limit. M-estimation is employed to estimate the unknown a of the model. In this paper, the consistent M-estimation is proved to be asymptotically normal and the optimal M-equation is obtained. Finally, a computation method is introduced to solve the M-equation and to get the optimal solution. |
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