Model Averaging Inference And Application For Multivariate Linear Regression Models

Model averaging methods avoid the uncertainty caused by the traditional model selection process through model combination.However,most of this work is focus on the uniresponse situation.In this paper,we consider the application of model averaging technology to multivariate linear regression,and provide model averaging solution based on two methods of dimension reduction.For the case where each candidate model is assumed to be the subset model,we propose a corrected Mahalanobis Mallows model averaging(MMMAc)method,and derive an unbiased estimator of the Mallows-type risk as a corrected weights selection criterion by constructing the Wishart distribution.Under certain conditions,we proved that the MMMAc estimators process the same asymptotic optimality as the Mahalanobis Mallows model averaging(MMMA)estimators.Simulation experiment verified the improvement of our MMMAc method.In order to make full use of information,and realized that the effect of a same covariate is always different for each responses,we propose a model averaging approach based on reduced-rank regression(RRRMA).The candidate models of this method is set as reduced-rank regression models.We first obtain the expression of the model averaging estimator in terms of canonical variables,and derive a Mallows-type weight selection criterion based on the asymptotic distribution of reduced-rank regression estimator.Then,the asymptotic optimality of the resulting model averaging estimator is proved under certain conditions.The competitive performance of our model averaging estimator is investigated in simulation experiments and real data analysis.