Electronic Journal of Statistics

Consistency of the posterior distribution and MLE for piecewise linear regression

Tristan Launay, Anne Philippe, and Sophie Lamarche

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Abstract

We prove the weak consistency of the posterior distribution and that of the Bayes estimator for a two-phase piecewise linear regression model where the break-point is unknown. We also establish a Bernstein-von Mises theorem for this non regular model. The non differentiability of the likelihood of the model with regard to the break-point parameter induces technical difficulties that we overcome by creating a regularised version of the problem at hand. We first recover the strong consistency of the quantities of interest for the regularised version, using results about the MLE, and we then prove that the regularised version and the original version of the problem share the same asymptotic properties.

Article information

Source
Electron. J. Statist., Volume 6 (2012), 1307-1357.

Dates
First available in Project Euclid: 26 July 2012

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1343310299

Digital Object Identifier
doi:10.1214/12-EJS713

Mathematical Reviews number (MathSciNet)
MR2988449

Zentralblatt MATH identifier
1336.62089

Keywords
Bayesian asymptotic Bernstein-von Mises theorem maximum-likelihood estimation non-regular model piecewise regression

Citation

Launay, Tristan; Philippe, Anne; Lamarche, Sophie. Consistency of the posterior distribution and MLE for piecewise linear regression. Electron. J. Statist. 6 (2012), 1307--1357. doi:10.1214/12-EJS713. https://projecteuclid.org/euclid.ejs/1343310299


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