SOME NOTES ON PARAMETER ESTIMATION IN A CLASS OF LINEAR MODELS WITH AN ERROR VECTOR HAVING MULTIVARIATE t DISTRIBUTION
误差服从多元t分布的一类线性模型下参数估计的若干注记

This paper studies some problems of parameter estimation in a class of linear models, which include the following common models: the multivariate linear model, the growth curve model, the extended growth curve model, the seemingly unrelated regression equations, the variance components model, and so on. It is proved that the class of linear models with multivariate t error terms and the one with multivariate normal error terms possess the same complete statistic and the same unbiased estimator, and that a sufficient statistic for the later models is also one for the former models. For the above several special models with the various covariance structures, the conclusions on the existence of the uniformly minimum risk unbiased(UMRU) estimators of the covariance matrix and concerned parameters under the error vector having multivariate normal distribution are extended to the case of the error vector having multivariate t distribution. Moreover, the C-R lower bound of the covariance matrix of the unbiased estimator for the estimable linear function of regression coefficients in the class of linear models with multivariate t error terms is given.