Optimal Prediction In The Linear Model And Its Robustness

Linear model is a vital class of statistical model which involves regression model, variance analysis model, covariance analysis model and mixed model etc. It is widely applied in biology, medicine, industry, agriculture, engineering, economics, administration etc. Morever, linear model's basic theory and methods are basic tools of other statistical ones. Specially, multivariate linear model and the general curve model are two classes important model of linear model.The prediction problem is to predict the unknown observation by using the known ones. In this paper, the conditional optimal prediction of the conditional predictable variable in the general growth curve model and linear equality constraints is investigated, which is unique with probability one, are obtained. And the simple projection predictor in the general growth curve model with different linear predictable variable is investigated. In addition, robustness of linear model optimal prediction are investigated. Robustness of the best linear unbiased prediction in the multivariate linear model with arbitrary bank are investigated. Necessary and sufficient conditions for the predictor of linear predictable variable to be robust with respect to covariance matrices are obtained, thus extending the results of robustness to the multivariate linear model with arbitrary bank and linear equality constraints, the general growth curve model, the general growth curve model with linear equality constraints. Finally, robustness of the simple projection predictor in the general growth curve model with different linear predictable variable on the covariance matrix are investigated.