广义线性模型中极大拟似然估计的强收敛速度

在sup_{i ≥1}E||y_i||^2+α < ∞(对某个α > 0)和其它正则条件下, 证明了一般联系函数的多维广义线性模型拟似然估计的强相合性, 并得到了强收敛速度, 其中 y_i 是响应变量. 此结果是对文献中相应结果的改进.

Strong Convergence Rates of the Maximum Quasi-Likelihood Estimator in Generalized Linear Models

In a generalized linear model with q×1 responses, bounded and fixed p×q regressors Z_i and general  link function, under  the moment condition on responses as weak as possible and other conditions, the authors prove that with probability one, the quasi-likelihood equation has a solution βn for all large sample size n. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.  This result is an  improvement over the relevant results in literature.