摘要
在生长曲线模型中,参数矩阵的最小二乘估计为响应变量的线性函数,而极大似然估计为响应变量的非线性函数,所以极大似然估计的统计推断比较复杂.为了使它的统计推断简单点,一些学者考虑了极大似然估计与最小二乘估计的等价性.不幸的是极大似然估计与最小二乘估计的完全等价性不易满足.因此考虑它们的近似等价性,即考虑它们基于欧式范数标准下的模长之比.如果比值在任意给定的允许误差之内,就认为极大似然估计近似等价于最小二乘估计,从而简化极大似然估计的统计推断.
In a growth curve model,the generalized least squares estimator of the parameter matrix is a linear function of the response variables while its maximum likelihood estimator is nonlinear,so the statistical inference based on the maximum likelihood estimate might be more complicated.In order to make its statistical inference more easily analytical and tractable to obtain,some authors concern conditions under which the maximum likelihood estimator is completely equivalent to the generalized least squares estimator.Unfortunately,such conditions are very parsimonious.Therefore,an asymptotical equivalence between them is suggested,that is,consider the ratio of two covariance matrices concerned based on Euclidean norm.It is believed that the maximum likelihood estimator approximates the generalized least squares estimator if the ratio between them is limited to the permitted errors,and then the statistical inference of the maximum likelihood estimator is simplified.
出处
《浙江工业大学学报》
CAS
2012年第2期233-236,共4页
Journal of Zhejiang University of Technology
基金
国家自然科学基金资助项目(11126211)
关键词
近似等价性
欧式范数
最小二乘估计
极大似然估计
生长曲线模型
approximate equivalence
Euclidean norm
generalized least square estimate
maximum likelihood estimate
growth curve model
