相依误差广义线性模型的M估计的Bahadur表示

Bahadur Representations of the M-estimation in GLMs with Dependent Errors

考虑如下广义线性模型y_i=h(x^T_i,β)+e_i=1,2,…,n,其中e_i=G(…,ε_(i-1),ε_i),h是一个连续可导函数,ε_i是独立同分布的随机变量,并且它的期望为0,方差σ~2有限.本文给出了参数β的M估计,并且得到了该估计的Bahadur表示,该结论推广了线性模型的相关结论.应用M估计的Bahadur表示,得到了相依误差的线性回归模型,poisson模型,logistic模型和独立误差的广义线性模型等模型的渐近性质.

The paper studies a generalized linear model （GLM） Yi = h（xi^Tβ） ＋ei, i = 1, 2,...,n, where e~ = G（...,εi-1,εi）, h is a continuous differentiable function, εi＇s are independent and identically distributed （i.i.d.） random errors with zero mean and finite variance a2. We consider the M-estimator of parameter /3 in the model, and investigate the Bahadur representations, which extend the correspondingly results of linear regression models to the generalized linear model. Moreover, by our results, it is easy to obtain the asymptotic properties of βn in some models, including linear regression models with dependent errors, poisson models with dependent errors, logistic models with dependent errors, and GLMs with i.i.d, errors. Keywords generalized linear models; M-estimator; Bahadur representations; dependent errors