variable selection of generalized semi-parametric mixture models


1 Department of Statistics, Allameh Tabataba’i University

2 Department of Statistics, Mashhad branch, Islamic Azad University

3 School of Mathematics, Iran University of Science and Technology


Purpose of this paper is identifying best covariates of a semi-parametric model in the presence of penalized coefficients. It should be noted that in each model, coefficients of the existing variables is considered as a combination of parameters where some of them affect the response variable linearly and some of them functionally. So, semi-parametric method was considered as an optimum solution.
In this paper we concerned with variable selection in finite mixture of generalized semi-parametric models. This task consists of model selection for nonparametric component and variable selection for parametric part. Thus we encounter with separate model selection for each nonparametric component of each sub model. To overcome to this computational burden, we introduce a class of variable selection procedures for finite mixture of generalized semi-parametric models. It is shown that the new method is consistent for variable selection. Simulations show that the performance of proposed method is good and improve pervious works in this area and also requires much less computing power than existing methods.


Main Subjects

[1]Breiman, L. (1996), Heuristics of instability and stabilization in model selection, The Annals of Statistics, 24, 2350–2383.
[2] Fan, J. and Li, R. (2001), Variable selection via nonconcave penalized likelihood and its oracle properties, J. Amer. Statist. Assoc.,
96, 1348-1360.
[3] Ma, S., Song, Q. and Wang, L. (2013), Simultaneous variable selection and estimation in semiparametric modeling of longitudinal/clustered data, Bernoulli, 19, 252-274.
[4] Tibshirani, R. (1996), Regression shrinkage and selection via
the lasso, J. Royal. Statist. Soc., Series B., 58, 267-288.
[5] Fan, J. and Li, R. (2002), Variable selection for cox's proportional hazards model and frailty model, Ann. Statist., 30, 74-99.