Asymptotic behavior of median estimators of multiple change points
Author:
G. Shurenkov
Translated by:
V. Semenov
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
MathSciNet review:
2110873
Full-text PDF Free Access
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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.
References
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- A. A. Borovkov, Asymptotically optimal solutions in a change-point problem, Teor. Veroyatnost. i Primenen. 43 (1998), no. 4, 625–654 (Russian, with Russian summary); English transl., Theory Probab. Appl. 43 (1999), no. 4, 539–561. MR 1692429, DOI https://doi.org/10.1137/S0040585X97977112
- R. E. Maĭboroda and O. V. Sugakova, The limit distribution of DP estimators of multiple change points. (to appear)
- O. V. Sugakova, A search for change points in a flow of independent observations, Teor. Ĭmovīr. Mat. Stat. 55 (1996), 167–172 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 55 (1997), 181–186 (1998). MR 1641589
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References
- R. E. Maĭboroda and O. V. Sugakova, A fast algorithm for detecting multiple change points, Teor. Ĭmovīr. Mat. Stat. 57 (1997), 103–108; English transl. in Theory Prob. Math. Statist. 57 (1998), 109–114. MR 1806888 (2003b:62100)
- A. A. Borovkov, Asymptotically optimal solutions in the change-point problem, Teor. Veroyatnost. Primenen. 43 (1998), no. 4, 625–654; English transl. in Theory Probab. Appl. 43 (1999), no. 4, 539–561. MR 1692429 (2001g:62044)
- R. E. Maĭboroda and O. V. Sugakova, The limit distribution of DP estimators of multiple change points. (to appear)
- O. V. Sugakova, A search for change points in a flow of independent observations, Teor. Ĭmovīr. Mat. Stat. 55 (1996), 167–172; English transl. in Theory Probab. Math. Statist. 55 (1997), 181–186. MR 1641589 (99g:62066)
- Marc Raimondo, Minimax estimation of sharp change points, Ann. Stat. 26 (1998), no. 4, 1379–1397. MR 1647673 (99i:62076)
- V. V. Mottl’, I. B. Muchnik, and V. G. Yakovlev, Optimal segmenting of experimental curves, Avtomat. i Telemekh. 8 (1983), 84–95. (Russian)
- R. E. Maĭboroda, The median estimator of disorder in the case of weakly dependent observations, Teor. Veroyatnost. i Mat. Statist. 43 (1990), 82–87; English transl. in Theory Probab. Math. Statist. 43 (1991), 87–91. MR 1069318 (91m:62079)
- V. N. Vapnik and A. Ya. Chervonenkis Theory of Pattern Recognition, “Nauka”, Moscow, 1974. (Russian) MR 0474638 (57:14274)
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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
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
