The limit distribution of dynamic programming estimators of multiple change points
Authors:
R. E. Maĭboroda and O. V. Sugakova
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 69 (2004), 103-113
MSC (2000):
Primary 62G20; Secondary 93E10
DOI:
https://doi.org/10.1090/S0094-9000-05-00618-6
Published electronically:
February 8, 2005
MathSciNet review:
2110909
Full-text PDF Free Access
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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.
References
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References
- L. Horváth, The maximum likelihood method for testing changes in the parameters of normal observations, Ann. Statist. 21 (1993), no. 2, 671–680. MR 1232511 (94k:62028)
- V. V. Mottl’, I. B. Muchnik, and V. G. Yakovlev, An optimal segmenting of experimental curves, Avtomat. i Telemekh. 8 (1983), 84–95; English transl. in Automat. Remote Contr. (1984).
- O. V. Sugakova, A search for change points in a flow of independent observations, Teor. Imovir. ta Matem. Statist. 55 (1996), 167–172; English transl. in Theor. Probab. and Math. Statist. 55 (1997), 181–186. MR 1641589 (99g:62066)
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Additional Information
R. E. Maĭboroda
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
Received by editor(s):
January 27, 2003
Published electronically:
February 8, 2005
Article copyright:
© Copyright 2005
American Mathematical Society
