A Note on the Adaptive LASSO for Zero-Inflated Poisson Regression

作     者：Banerjee, Prithish Garai, Broti Mallick, Himel Chowdhury, Shrabanti Chatterjee, Saptarshi 

作者机构：JP Morgan Chase & Co New York NY USA NBCUniversal New York NY USA Harvard TH Chan Sch Publ Hlth Dept Biostat Boston MA 02115 USA Broad Inst MIT & Harvard Program Med & Populat Genet Cambridge MA 02142 USA Icahn Sch Med Mt Sinai Dept Genet & Genom Sci New York NY 10029 USA Eli Lilly & Co Indianapolis IN 46285 USA 

出 版 物：《JOURNAL OF PROBABILITY AND STATISTICS》 (概率论与统计杂志)

年 卷 期：2018年第2018卷第1期

页      面：1-9页

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：University of Alabama  UA 

主　　题：ZERO-inflated probability distribution POISSON regression PARAMETER estimation EXPECTATION-maximization algorithms REGULARIZATION parameter 

摘      要：We consider the problem of modelling count data with excess zeros using Zero-Inflated Poisson (ZIP) regression. Recently, various regularization methods have been developed for variable selection in ZIP models. Among these, EM LASSO is a popular method for simultaneous variable selection and parameter estimation. However, EM LASSO suffers from estimation inefficiency and selection inconsistency. To remedy these problems, we propose a set of EM adaptive LASSO methods using a variety of data-adaptive weights. We show theoretically that the new methods are able to identify the true model consistently, and the resulting estimators can be as efficient as oracle. The methods are further evaluated through extensive synthetic experiments and applied to a German health care demand dataset.