线性再生散度模型的极大L_(q)-似然估计的渐近性质

Asymptotic properties of the maximum L_(q)-likelihood estimates in linear reproductive dispersion models

线性再生散度模型是线性回归模型、广义线性模型和指数线性模型的自然推广,极大L_(q)-似然估计是基于非广义熵的新参数估计方法,是极大似然估计的推广。用极大L_(q)-似然估计研究线性再生散度模型,在一定的条件下,给出了线性再生散度模型的极大L_(q)-似然估计的弱相合性和渐近正态性。最后通过模拟算例表明:随着n的增大参数估计值越接近真值;当q→1时,ML_(q)E的参数估计值接近于MLE的参数估计值。

Linear reproductive dispersion models(LRDMS)are the natural generalization of linear regression models,generalized linear models and exponential linear models.Maximum L_(q)-likelihood estimator(ML_(q)E)is a new parametric estimator based on nonextensive entropy,which is a generalization of maximum likelihood estimation.In this paper,ML_(q)E is used to study LRDM,the weak consistency and asymptotic normality of ML_(q)E of RDLM are obtained under certain assumptions.Finally,it is illustrated by a simulation example:parametric estimator gets closer to the true value with the increasing of n,and the parametric estimator of ML_(q)E is close to the parameter estimate of MLE.