Statistics Inference Of Variance Components In Mixed Linear Model

In this paper, we mainly discuss variance components' estimators, nonnegative improvement ,test and relative problems in mixed linear model with two variance components,some new results were obtained. For variance components model,we propose variance components' quadratic invariant estimator and generalized spectral decomposition estimator. We obtain estimator class which have properites of unbiased and invariant, we analysis the problem of improvement estimator based on variance componentsσ_u~2's estimator class. Under mean square errors,we give up unbiased constructing nonnegative improvement .We gain nonnegative quadratic invariant estimator class which not only have smaller mean square error than quadratic invariant unbiased estimators ,but superior to ANOVA and UMVUE .Meanwhile ,we establish the necessary and sufficient conditions for the existence of nonnegative improvement.Futhermore,we consider the conditions of equality among quadratic estimator ,generalized spectral decomposition estimator and ANOVA, these estimators are UMVUE and give a very simply computation method of UMVUE .Finally ,under random regression coefficient model ,we discuss probability of variance components estimator with negative value and tests,and these tests are UMPUT.