Simultaneous Prediction In Generalized Linear Regression Model And Its Properties

Not confined to the assumption of irrelevance and homovariance of error,generalized linear regression model is the basis of other statistical models and is still widely applied in various fields.In the context of simultaneously predicting the true value of the dependent variable and its mean value in practice,the simultaneous prediction and its properties under different criteria are studied.Under the quadratic loss,the BLUSP(best linear unbiased simultaneous prediction)is obtained.The BLUSP is superior to the BLUP(best linear unbiased prediction)and the SPP(simple projection prediction)of dependent variables.The leave-one-out cross validation method is proposed to select the weight in the simultaneous prediction.In homogeneous and inhomogeneous linear prediction classes,the necessary and sufficient conditions for the admissibility of simultaneous prediction are obtained respectively.Under the matrix loss,the necessary and sufficient conditions for the simultaneous prediction to be admissible are obtained respectively in homogeneous and inhomogeneous linear prediction classes.The BLUSP and its priority under matrix loss is obtained.By adjusting the weight in the simultaneous prediction,some properties of the true value and its mean of the dependent variable under quadratic and matrix loss function are verified.Considering the accuracy and the goodness fit of the predicting model,the balanced loss function is proposed to derive the prediction.Under this criterion and its improved form,the BLUP and its admissibility are obtained for the dependent variable and its linear function,also for the function of simultaneous prediction under the quadratic loss function.Through numerical simulations,for the generalized linear regression model with two probability distributions of error terms,the BLUP,SPP and BLUSP are described.Nu-merical simulations verify that the leave-one-out cross validation method to determine the weight in the simultaneous prediction is feasible.Finally,the priority of the best linear un-biased simultaneous prediction is verified.The relationship between a set of trade data is studied.Under the assumption of generalized linear regression model with two probabili-ty distributions of error terms,the weight in the simultaneous prediction is selected by the leave-one-out cross validation method.