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Stochastic search for semiparametric linear regression models

Lutz Dümbgen, Richard J. Samworth, and Dominic Schuhmacher

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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.

Chapter information

Source
Banerjee, M., Bunea, F., Huang, J., Koltchinskii, V., and Maathuis, M. H., eds., From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2013) , 78-90

Dates
First available in Project Euclid: 8 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1362751181

Digital Object Identifier
doi:10.1214/12-IMSCOLL907

Zentralblatt MATH identifier
1327.62204

Subjects
Primary: 62G05: Estimation 62G09: Resampling methods 62G20: Asymptotic properties 62J05: Linear regression

Rights
Copyright © 2010, Institute of Mathematical Statistics

Citation

Dümbgen, Lutz; Samworth, Richard J.; Schuhmacher, Dominic. Stochastic search for semiparametric linear regression models. From Probability to Statistics and Back: High-Dimensional Models and Processes -- A Festschrift in Honor of Jon A. Wellner, 78--90, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2013. doi:10.1214/12-IMSCOLL907. https://projecteuclid.org/euclid.imsc/1362751181


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