The Model Average Of The Gaussian Mixture Model

As an alternative to variable selection(or model selection),model averaging has recently received a great deal of attention.Model averaging usually reduces the risk in regression estimation,as "betting" on multiple models provides a type of insurance against a singly selected model being poor and avoiding ignoring useful information from the form of the relationship between response and covariates.Particularly,model averaging often improves estimation accuracy when the underlying model is unstable with a high noise level.At present,model averaging develops mainly in two directions: Bayesian model averaging and Frequentist model averaging.In this paper,the bayesian model averaging and frequentist model averaging are briefly introduced at first and the simulation studies are used to compare the performance of the model averaging methods mentioned above under linear and generalized linear models.As we all know,existing model averaging methods are developed around linear and generalized linear models mainly,but the research on model averaging of gaussian mixture model still has a lot of works to be done.Therefore,this paper further extends the model averaging to the gaussian mixture model,proposes a frequentist model averaging method for selecting weights based on J-fold cross validation criteria,and the asymptotic optimality of the model averaging estimator is proved.This contribution has widened the existing research results on the model averaging theories.In addition to theoretical findings,this paper also contains a large amount of simulation results and empirical example to demonstrate the risk of the proposed model averaging estimator is relatively low in most cases.