The strong consistency of M-estimates of the regression coefficients in a linear model under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment condition. Especially, in some important circumstances, onlyE|ψ(ek)|q for some q > 1 is needed, where ψ{ek} is some score function of random error.
Rao and Zhao (1992) used random weighting method to derive the approximate distribution of the M-estimator in linear regression model.In this paper we extend the result to the censored regression model (or censored “Tobit” model).
In this paper, we propose an information-theoretic-criterion-based modelselection procedure for log-linear model of contingency tables under multinomial sampling, andestablish the strong consistency of the method under some mild conditions. An exponential bound ofmiss detection probability is also obtained. The selection procedure is modified so that it can beused in practice. Simulation shows that the modified method is valid. To avoid selecting the penaltycoefficient in the information criteria, an alternative selection procedure is given.
ZHAO Lincheng ZHANG Hong(University of Science and Technology of China, Hefei, Anhui 230026. China)
A regression model with a nonnegativity constraint on the dependent variable,known as censored median regression model, is considered. Under some mild conditions, the LAD estimate of the regression coefficient is shown to be strongly consistent.Furthermore, its convergence rate and Bahadur strong representation are also obtained.
BRPA估计是Changchien(1990)提出的一种具有良好性质的回归函数最大值点的估计,Chen, Huang and Huang(1996),Bai and Huang(1999),吴and王(2000)和Bai,Chen and Wu(2003) 分别讨论了BRPA的极限性质．本篇文章中,我们在很一般的条件下研究了x为多维向量时BRPA 估计的收敛速度,推广了Bai,Chen and Wu(2003)的结果．
