The length of the interval of indeterminacy for the estimate of multiple change-points
Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 251-266.

Voir la notice de l'article provenant de la source Math-Net.Ru

This article considers the problem of estimating the length of the interval of indeterminacy during construction of change-points' estimates using dynamical programming. It was proved that mathematical expectation of the length of the interval has asymptotically linear dependency on the penalty for a change of distribution when the number of estimations tends to infinity.
Keywords: Change-points, dynamical programming.
@article{THSP_2007_13_2_a8,
     author = {Grigorij Shurenkov},
     title = {The length of the interval of indeterminacy for the estimate of multiple change-points},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {251--266},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a8/}
}
TY  - JOUR
AU  - Grigorij Shurenkov
TI  - The length of the interval of indeterminacy for the estimate of multiple change-points
JO  - Teoriâ slučajnyh processov
PY  - 2007
SP  - 251
EP  - 266
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a8/
LA  - en
ID  - THSP_2007_13_2_a8
ER  - 
%0 Journal Article
%A Grigorij Shurenkov
%T The length of the interval of indeterminacy for the estimate of multiple change-points
%J Teoriâ slučajnyh processov
%D 2007
%P 251-266
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a8/
%G en
%F THSP_2007_13_2_a8
Grigorij Shurenkov. The length of the interval of indeterminacy for the estimate of multiple change-points. Teoriâ slučajnyh processov, Tome 13 (2007) no. 2, pp. 251-266. http://geodesic.mathdoc.fr/item/THSP_2007_13_2_a8/

[1] A. A. Borovkov, “Asymptotically optimal solutions of the problem of changepoints”, Theory of probability and its applications, 43:4 (1998), 625-–654

[2] R. E. Mayboroda, O. V. Sugakova, “Limit distribution of DP-estimates of multiple change-moments”, Tjeory of hrobability and mathematical statistics, 69 (2003), 96-105

[3] B. Yakir, A. M. Krieger, M. Pollak, “Detecting change in regression: first order optimality”, The Annals of Statistics, 27:6 (1999), 2179-–2205

[4] H. V. Poor, “Quickest detection with exponential penalty for delay”, The Annals of Statistics, 26:6 (1998), 2176-–2205

[5] C. R. Loader, “Change point estimation using nonparametric regression”, The Annals of Statistics, 24:4 (1996), 1667-–1678

[6] V. V.Mottl, I. V. Muchnik, V. G. Yakovlev, “Optimal segmentation of experimental curves”, Automatics and telemechanics, 1983, no. 8, 84-95

[7] O. V. Sugakove, “The search for change-points inthr flow of independent observations”, Theory of probability and mathematical statistics, 55 (1997), 181-–186

[8] G. V. Shurenkov, Length of interval of indeterminacy in change-poits estimation using dynamic programming algorithm