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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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.

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

First available in Project Euclid: 26 July 2012

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


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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