Stochastic search for semiparametric linear regression models

Dümbgen, Lutz; Samworth, Richard J.; Schuhmacher, Dominic

doi:10.1214/12-IMSCOLL907

VOL. 9 | 2013 Stochastic search for semiparametric linear regression models

Chapter Author(s) Lutz Dümbgen, Richard J. Samworth, Dominic Schuhmacher

Editor(s) M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, M. H. Maathuis

Inst. Math. Stat. (IMS) Collect., 2013: 78-90 (2013) DOI: 10.1214/12-IMSCOLL907

Abstract

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [ Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [ Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.