Theory Of Estimation And Prediction In Several Statistical Models

The thesis is concerned with statistical inferences including parameter esti-mation and prediction of future observations in finite populations under severalstatistical models.For general linear mixed models, the estimation of a linear combination offixed and random e?ects is investigated. Explicit expression of the best linearunbiased estimator(BLUE) of the combination is derived and we show that thisBLUE is essentially-unique where the covariance matrix of the vector of obser-vations may be singular. For the three small-area models which are all specialcases of the general linear mixed model, we derive spectral decomposition estima-tors(SDE) of small area mean. Furthermore, second-order approximations to theMSE of two-stage estimators based on SDE of variance components are obtainedunder normality. Noting that in the general linear mixed model with two vari-ance components and the balanced linear mixed model of multi-way classificationrandom e?ects, the covariance matrix of observation vector has special structure,and using the linear transformation for original model by idempotent matricesin the spectral decomposition of the covariance matrix, the problem of estima-tion of the covariance matrix becomes simultaneous estimation of all the distincteigenvalues of it. We provide a class of the spectral decomposition estimators ofthe covariance matrix, and the best invariant estimator is obtained in this class.By using statistical decision theoretic approach, we investigate the domination of...