Bernoulli

  • Bernoulli
  • Volume 16, Number 3 (2010), 759-779.

Asymptotic properties of maximum likelihood estimators in models with multiple change points

Heping He and Thomas A. Severini

Full-text: Open access

Abstract

Models with multiple change points are used in many fields; however, the theoretical properties of maximum likelihood estimators of such models have received relatively little attention. The goal of this paper is to establish the asymptotic properties of maximum likelihood estimators of the parameters of a multiple change-point model for a general class of models in which the form of the distribution can change from segment to segment and in which, possibly, there are parameters that are common to all segments. Consistency of the maximum likelihood estimators of the change points is established and the rate of convergence is determined; the asymptotic distribution of the maximum likelihood estimators of the parameters of the within-segment distributions is also derived. Since the approach used in single change-point models is not easily extended to multiple change-point models, these results require the introduction of those tools for analyzing the likelihood function in a multiple change-point model.

Article information

Source
Bernoulli, Volume 16, Number 3 (2010), 759-779.

Dates
First available in Project Euclid: 6 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1281099883

Digital Object Identifier
doi:10.3150/09-BEJ232

Mathematical Reviews number (MathSciNet)
MR2730647

Zentralblatt MATH identifier
1220.62021

Keywords
change-point fraction common parameter consistency convergence rate Kullback–Leibler distance within-segment parameter

Citation

He, Heping; Severini, Thomas A. Asymptotic properties of maximum likelihood estimators in models with multiple change points. Bernoulli 16 (2010), no. 3, 759--779. doi:10.3150/09-BEJ232. https://projecteuclid.org/euclid.bj/1281099883


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