Conditional Sure Independent Screening Based On Finite Mixture Model

When the response variables are no longer content to obey the assumption of a single model,use of Finite mixture regression model fitting the data more accord with common sense,as covariate dimension pn is very high,usually only a few forecast variables contribute to response,the equivalent of ideally can assume parameter vector β is sparse.In the existing literature,penalty variable selection methods are usually used for high-dimensional Finite mixture model,such as LASSO,SCAD,Hard,etc.However,with the further increase of the dimension of variables,the traditional variable selection methods become unsuitable for ultrahigh-dimensional cases.For ultra-high-dimensional cases,Fan proposed marginal screening methods for linear model,generalized linear model,and generalized additive model.The idea of these methods is to reduce the data from ultra-high-dimensional to the dimension applicable to traditional variable selection.In this way,we can get better results when making further variable selection.Later,statisticians proposed a series of conditional marginal screening methods based on previously known important variables.When researchers learned from previous research results that some variables X contributed to the response,they took these prior information into account and then used this information to screen the remaining variables.In this paper,a conditional marginal screening method is proposed for Finite mixture models in the case of ultra-high dimension.The importance of variables is judged by the conditional marginal effect of variables,so as to achieve the effect of reducing the dimension.Considering LASSO variable selection method,a variable selection method CSIS-LASSO based on conditional sure independent screening is proposed.The results show that the conditional marginal parameter estimation has consistency.When the sample size is large enough,the conditional marginal parameter estimation of variables unrelated to the conditional marginal of response variables tends to 0 with probability 1,and the conditional marginal parameter estimation has asymptotic normality.The parameter estimation obtained by The CSIS-LASSO method satisfies the consistency and sparsity.Numerical simulation results show that the conditional sure independent screening method is effective in variable selection,and the CSIS-Lasso method is better in variable selection.