正态条件下带AR(1)-型方差结构GMANOVA-MANOVA模型极大似然估计的小样本特征

Finite Sample Properties of Maximum Likelihood Estimator for a GMANOVA-MANOVA Model with Normal Error and AR(1)Type Covariance Structure

研究了一类带一阶自回归(AR(1))-型方差结构的广义多元方差分析-多元方差分析(GMANO VA-MANOVA)模型参数极大似然估计的小样本特征.对带AR(1)-型方差结构GMANOVA-MANOVA模型,文章在正态条件下给出了参数极大似然估计存在的一个充分必要条件,讨论了极大似然估计唯一的充分条件.在该充分条件下,文章证明了相关系数极大似然估计的精确分布只与相关系数有关,并依此给出了自相关系数简单假设H0:ρ=0v.s.H1:ρ≠0的一个不需要叠代计算估计的检验,同时模拟表明该检验为无偏检验且势函数与似然比检验势函数无太大差异.

In this paper,we study the finite sample properties of maximum likelihood estimator(MLE) of generalized multivariate analysis of variance-multivariate analysis of variance(GMANOVA-MANOVA) model with the first order-autoregressive(AR(1)) type covariance structure.We provide the necessary condition for the existence of maximum likelihood estimator in GMANOVA-MANOVA models and a sufficient condition for the uniqueness of the maximum likelihood estimator is also studied.Under the provided sufficient condition,we show that the exact distribution of the maximum likelihood estimator of the correlation coefficient only depends on the true value of p.In addition,we propose a simple hypothesis test for testing H0:ρ=0 v.s.H1:ρ≠0,which does not require any iteration procedures.Simulation shows that the proposed hypothesis test is unbiased and has very comparable power to that of the likelihood ratio test.