## Electronic Journal of Statistics

### Joint estimation and variable selection for mean and dispersion in proper dispersion models

#### Abstract

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.

#### Article information

Source
Electron. J. Statist., Volume 10, Number 1 (2016), 1630-1676.

Dates
First available in Project Euclid: 18 July 2016

https://projecteuclid.org/euclid.ejs/1468847266

Digital Object Identifier
doi:10.1214/16-EJS1152

Mathematical Reviews number (MathSciNet)
MR3522656

Zentralblatt MATH identifier
06624497

#### Citation

Antoniadis, Anestis; Gijbels, Irène; Lambert-Lacroix, Sophie; Poggi, Jean-Michel. Joint estimation and variable selection for mean and dispersion in proper dispersion models. Electron. J. Statist. 10 (2016), no. 1, 1630--1676. doi:10.1214/16-EJS1152. https://projecteuclid.org/euclid.ejs/1468847266

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