The Study On Utilizing Linear Regression To Prediction

Prediction is widely applied in economics,biology,industry,agriculture,medicine,national defence etc. Prediction must be based on models. Linear regression model is one of prediction models. This thesis studies on utilizing multivariate linear regression to prediction.First, consider the multivariate linear regression model 0 0 0Y XBY X Bεε??? == ++, (A) Under the relative error criteria, we give the definition of minimax estimation of Y0 and find minimax estimation of Y0 .Meanwhile we prove the minimax estimation of Y0 is unbiased . Next ,according to model (3.1),(3.2) we give the following assumptions: Assumption 1: E[ V ec (ε)] = 0, Assumption 2: V [V ec (ε)]=σ2Δ?Σ, Assumption 3: E[ V ec(ε0)] = 0, Assumption 4: V [V ec (ε0 )]=σ2Δ?Σ0, Assumption 5: E[ V ec (ε)V ec′(ε0)]=σ2Δ? V, Assumption 6:∑0 ?V′∑?1V≠0, whereσ2 is unknown parameter,Δis q×q known positive definite matrix,Σis n×n known positive definite matrix, V is n×m known matrix,Σ0 is m×m known positive definite matrix. The above model is called model(B).Under model(B) we obtain the optimal prediction matrix of Y0 .