The purpose of this paper is to study Bayesian like R- and M-estimators of change point(s). These estimators have smaller variance than the related argmax type estimators. Confidence intervals for the change point based on the exchangeability arguments are constructed. Finally, theoretical results are illustrated on the real data set.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1007,
author = {Jarom\'\i r Antoch and Marie Huskov\'a},
title = {Bayesian like R- and M- estimators of change points},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {20},
year = {2000},
pages = {115-134},
zbl = {0971.62010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1007}
}
Jaromír Antoch; Marie Husková. Bayesian like R- and M- estimators of change points. Discussiones Mathematicae Probability and Statistics, Tome 20 (2000) pp. 115-134. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1007/
[000] [1] J. Antoch and M. Husková, Estimators of changes, Nonparametrics, Asymptotics and Time Series, Ghosh S. ed., M. Dekker, (1998a), 533-578. | Zbl 1069.62515
[001] [2] J. Antoch and M. Husková, Bayesian like estimators of changes, 1998b, J. Stat. Plan. Infer., submitted. | Zbl 1069.62515
[002] [3] J. Antoch and J.Á. Vísek, Robust estimation in linear model and its computational aspects, Computational Aspects of Model Choice, Physica Verlag, Heidelberg, Antoch J. ed., (1992), 39-104.
[003] [4] G.W. Cobb, The problem of the Nile: Conditional solution to a change-point problem, Biometrika 65 (1978), 243-251. | Zbl 0394.62074
[004] [5] M. Csörgo and L. Horváth, Limit Theorems in Change-Point Analysis, J. Wiley, New York 1997.
[005] [6] L. Dümbgen, The asymptotic behavior of some nonparametric change-point estimators, Ann. Statist. 19 (1991), 1471-1495. | Zbl 0776.62032
[006] [7] E. Gombay and M. Husková, Rank based estimators of the change-point, J. Stat. Plan. Infer. 67 (1997), 137-154. | Zbl 0932.62038
[007] [8] D. Hinkley and E. Schechtman, Conditional bootstrap methods in the mean-shift model, Biometrika 74 (1987), 85-93. | Zbl 0604.62036
[008] [9] P. J. Huber, Robust Statitics, J. Wiley, New York 1981.
[009] [10] M. Husková, Limit theorems for rank statistics, Statist. and Probab. Letters 30 (1997a), 45-55.
[010] [11] M. Husková, Limit theorems for M-processes via rank statistics processes, Advances in Combinatorial Methods with Applications to Probability and Statistics, Balakrishnan N. ed., (1997b), 527-533.
[011] [12] M. Husková, Multivariate rank statistics processes and change-point analysis, Volume of Saleh, 1997c (to appear).
[012] [13] I. A. Ibragimov and R. Z. Has'minskii, Statistical Estimation. Asymptotic Theory, Springer Verlag, Heidelberg 1981.
[013] [14] Y. Ritov, Asymptotic efficient estimation of the change-point with unknown distribution, Ann. Statist. 18 (1990), 1829-1839. | Zbl 0714.62027