The limit distribution of dynamic programming estimators of multiple change points

Authors:
R. E. Maiboroda and O. V. Sugakova

Translated by:
S. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **69** (2003).

Journal:
Theor. Probability and Math. Statist. **69** (2004), 103-113

MSC (2000):
Primary 62G20; Secondary 93E10

Published electronically:
February 8, 2005

MathSciNet review:
2110909

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider a problem of estimating multiple change points in the case where the distributions of observations between change points belong to a finite family of known distributions. We describe a dynamic programming procedure of the estimation and a method for improving estimators that generalizes the averaged likelihood method. The limit distributions of these estimators are given in terms of the argument of the minimum of random walks. We show that these distributions, for an appropriate set of parameters, coincide with those of the maximum likelihood estimators or averaged likelihood estimator for models with only one change point.

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Additional Information

**R. E. Maiboroda**

Affiliation:
Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrs’ka Street 63, Kyiv, Ukraine

Email:
mre@mechmat.univ.kiev.ua

**O. V. Sugakova**

Affiliation:
Faculty for Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrs’ka Street 63, Kyiv, Ukraine

Email:
sugak@univ.kiev.ua

DOI:
https://doi.org/10.1090/S0094-9000-05-00618-6

Received by editor(s):
January 27, 2003

Published electronically:
February 8, 2005

Article copyright:
© Copyright 2005
American Mathematical Society