文章基本信息

标题：Joint estimation and variable selection for mean and dispersion in proper dispersion models
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作者：Anestis Antoniadis ; Irène Gijbels ; Sophie Lambert-Lacroix 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2016
卷号：10
期号：1
页码：1630-1676
DOI：10.1214/16-EJS1152
语种：English
出版社：Institute of Mathematical Statistics
摘要：When describing adequately complex data structures one is often confronted with the fact that mean as well as variance (or more generally dispersion) is highly influenced by some covariates. Drawbacks of the available methods is that they are often based on approximations and hence a theoretical study should deal with also studying these approximations. This however is often ignored, making the statistical inference incomplete. In the proposed framework of double generalized modelling based on proper dispersion models we avoid this drawback and as such are in a good position to use recent results on Bregman divergence for establishing theoretical results for the proposed estimators in fairly general settings. We also study variable selection when there is a large number of covariates, with this number possibly tending to infinity with the sample size. The proposed estimation and selection procedure is investigated via a simulation study, that includes also a comparative study with competitors. The use of the methods is illustrated via some real data applications.
关键词：Bregman divergence;Fisher-orthogonality;pe nalization;proper dispersion models;variable selection;scad.