负二项回归模型的重对数律和强相合性

Law of Iterated Logarithm and Strong Consistency for Negative Binomial Regression Model

本文构建负二项回归模型选择架构,研究在模型选择中对数似然函数的渐近性质及其与联系函数之间的依赖关系;推出模型参数最大似然估计的重对数律,并建立该类模型选择的强相合准则;证明在一些条件下,如果惩罚项阶数随模型的维数增加且介于O(lnln n)和O(n)之间,则由负最大对数似然和其惩罚项组成的模型选择准则几乎必然选择最简单的正确模型。

The structure of negative binomial regression model selection is constructed,and the asymptotic properties of logarithmic likelihood function and its dependence on relation function in model selection are studied.The law of iterated logarithm for maximum likelihood estimation of model parameters is derived,and the strong consistency criterion for selecting such models is established.It is proved that under some general conditions,if the order of penalty terms increases with the dimension of the model and is between O(lnln n)and O(n),the model selection criterion consisting of negative maximum logarithmic likelihood and penalty terms almost necessarily chooses the simplest correct model.