Several Studies On The Optimal Prediction Of Linear Statistical Model

Linear model is a kind of statistical model widely used in biology, economics, medicine, industry, agriculture and many other areas.Many phenomenas in these areas can use linear models to simulate and study.Therefore, the linear model has become indispensable tools in the field of data processing.Because of its widespread application value, the study of linear model has been made more systematic. The prediction problem is to predict the unknown observation by using the known ones, which is required in the study.Many researchers have obtained some excellent achievements.Based on the previous studies of the optimal linear prediction model, this paper gave further explore on the study of classical prediction, optimal heterogeneous prediction and optimal homogeneous prediction on the field of the superiority comparison. Under the condition of the full column rank linear model, and the historical data and the predicted values are linearly independent, this paper demonstrates the superiority relationship of predictors between quadratic hazard functions and mean dispersion error matrix. That means the quadratic hazard functions and mean dispersion error matrix of the predictor have the same half-order. If the linear model is a full column rank, and the historical data and the predicted values are linearly correlated, this paper demonstrates the superiority relationship of hetero-geneous prediction, homogeneous prediction and unbiased homogeneous prediction. Relevant theories on optimal prediction of linear model are perfected in the paper. Introducing ideas of mean dispersion error matrix, this paper defined y,-superiority and X,β-superiority for the predictor. Under the condition of the definition above, this paper constructed a biased predictor, derive the conditions under which the biased predictor is superior to the classical predictor in the aspects of mean square error matrix, and give detailed arguments.