多维广义线性模型拟似然估计的渐近正态性

对多维自适应设计广义线性模型中形如sum from i=1 to n xi(yi-μ(x′iβ))=0的拟似然方程,在limn→∞■~(3/4)/■=0和其他一些正则性的假定之下,论文证明了上述拟似然方程的解,即极大拟似然估计的渐近正态性,此结果推广和改善了文4]中的相关结果,其中■和■分别为sum from i=1 to n xix′i的最小特征根和最大特征根,x是有界的p×q阶设计矩阵.

Asymptotic normality of quasi-likelihood estimator in multivariate generalied linear model

For the quasi-likelihood equation sum from i=1 to n xi(yi-μ(x′i β))=0 in multivariate generalized linear model with adaptive design,under limn→∞■~(3/4)/■=0 and some regular assumptions,we proved that asymptotic normality of solution of the above equation(i.e.,maximum quasi-likelihood estimator),which extended and improved the result of the literature3],where ■ and ■ denoted minimum eigenvalue and maximum eigenvalue of sum from i=1 to n xix′i respectively,xi was a bounded p×q design matrix.