Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 6 (2012), 1307-1357.
Consistency of the posterior distribution and MLE for piecewise linear regression
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.
Electron. J. Statist., Volume 6 (2012), 1307-1357.
First available in Project Euclid: 26 July 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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