Model Selection Based On Mean Variance Simultaneous Regression

Mean-Variance regression model is abbreviated as MVR model.For real data,when we perform regression analysis,the problem we often face is the lack of effective prior information.For the model which does not satisfy the Gauss-Markov hypothesis,the accuracy of the parameters obtained by OLS method is very low.In the high dimension situation,we also face the problem of model selection.Therefore,based on MVR model,this paper adaptively weights the possible heteroscedasticity to eliminate the problem of large variation caused by heteroscedasticity;at the same time,the SCAD penalty term is introduced to MVR model for model selection,and it is proved that the estimated parameters of MVR-SCAD model satisfy Oracle properties(sparsity and asymptotic normality).Combining Newton method and LLA algorithm,an effective algorithm is proposed to solve the parameters,and we apply our model to an example of stock value prediction.