Asymptotic behavior of median estimators of multiple change points

Author:
G. Shurenkov

Translated by:
V. Semenov

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **70** (2004).

Journal:
Theor. Probability and Math. Statist. **70** (2005), 167-176

MSC (2000):
Primary 62G20; Secondary 94A13

DOI:
https://doi.org/10.1090/S0094-9000-05-00640-X

Published electronically:
August 12, 2005

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the problem of posterior estimation of multiple change points in the case of only two distributions. We find the asymptotic distribution of the difference between the median estimator of a single change point and the true change point and show that the distribution does not change if the unknown parameter is estimated by a median of the sample. We generalize the results to the case of multiple change points.

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Additional Information

**G. Shurenkov**

Affiliation:
Department of Probability Theory and Mathematical Statistics, Mechanics and Mathematics Faculty, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine

Email:
skorohod@i.com.ua

DOI:
https://doi.org/10.1090/S0094-9000-05-00640-X

Keywords:
Estimation of change points,
limit distribution,
dynamic programming algorithm,
sampling median

Received by editor(s):
March 14, 2003

Published electronically:
August 12, 2005

Article copyright:
© Copyright 2005
American Mathematical Society