Geodesic
Multiscale approach for change point detection
Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 774-804 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we present a multiscale approach for change point detection. The algorithm estimates likelihood-ratio (LR) test in several scrolling windows simultaneously. This makes the method adaptive to structural breaks of different scales. Critical values are calibrated in a data-driven way using multiplier bootstrap, which estimates nonasymptotic distribution of the test statistics.
Keywords: multiscale change point detection, multiplier bootstrap, scrolling window, likelihood ratio test. 
@article{TVP_2016_61_4_a7,
     author = {A. L. Suvorikova and V. G. Spokoiny},
     title = {Multiscale approach for change point detection},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {774--804},
     year = {2016},
     volume = {61},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a7/}
}
TY  - JOUR
AU  - A. L. Suvorikova
AU  - V. G. Spokoiny
TI  - Multiscale approach for change point detection
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2016
SP  - 774
EP  - 804
VL  - 61
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a7/
LA  - ru
ID  - TVP_2016_61_4_a7
ER  - 
%0 Journal Article
%A A. L. Suvorikova
%A V. G. Spokoiny
%T Multiscale approach for change point detection
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2016
%P 774-804
%V 61
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a7/
%G ru
%F TVP_2016_61_4_a7
A. L. Suvorikova; V. G. Spokoiny. Multiscale approach for change point detection. Teoriâ veroâtnostej i ee primeneniâ, Tome 61 (2016) no. 4, pp. 774-804. http://geodesic.mathdoc.fr/item/TVP_2016_61_4_a7/

[1] Chernozhukov V., Chetverikov D., Kato K., “Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors”, Ann. Statist., 41:6 (2013), 2786–2819 | DOI | MR | Zbl

[2] Chernozhukov V., Chetverikov D., Kato K., “Comparison and anti-concentration bounds for maxima of Gaussian random vectors”, Probab. Theory Related Fields, 162:1–2 (2014), 47–70 | MR

[3] Fan J., Zhang C., Zhang J., “Generalized likelihood ratio statistics and Wilks phenomenon”, Ann. Statist., 29:1 (2001), 153–193 | DOI | MR | Zbl

[4] Frick K., Munk A., Sieling H., “Multiscale change point inference.”, J. Roy. Statist. Soc. Ser. B (Statist. Methodology), 76:3 (2014), 495–580 | DOI | MR

[5] Gallagher C., Lund R., Robbins M. W., “Changepoint detection in climate time series with long-term trends”, J. Climate, 26:14 (2013), 4994–5006 | DOI

[6] Lindeberg J. W., “Eine neue Herleitung des Exponentialgesetzes in der Wahrscheinlichkeitsrechnung”, Math. Z., 15:1 (1922), 211–225 | DOI | MR | Zbl

[7] Shiryaev A. N., Zhitlukhin M. V., Ziemba W. T., “Land and stock bubbles, crashes and exit strategies in Japan circa 1990 and in 2013”, Quantitative Finance, 15:9 (2015), 1449–1469 | DOI | MR

[8] Spokoiny V., “Parametric estimation. Finite sample theory”, Ann.Statist., 40:6 (2012), 2877–2909 | DOI | MR | Zbl

[9] Spokoiny V., Bernstein–von Mises theorem for growing parameter dimension, arXiv: 1302.3430

[10] Spokoiny V., Zhilova M., “Sharp deviation bounds for quadratic forms”, Math. Methods Statist., 22:2 (2013), 100–113 | DOI | MR | Zbl

[11] Spokoiny V., Zhilova M., “Bootstrap confidence sets under model misspecification”, Ann. Statist., 43:6 (2015), 2653–2675 | DOI | MR | Zbl

[12] Spokoiny V., “Multiscale local change point detection with applications to value-at-risk”, Ann. Statist., 37:3 (2009), 1405–1436 | DOI | MR | Zbl

[13] Wilks S. S., “The large-sample distribution of the likelihood ratio for testing composite hypotheses”, Ann. Math. Statist., 9:1 (1938), 60–62 | DOI

[14] Zhang N. R., Siegmund D. O., Ji H., Li J. Z., “Detecting simultaneous change points in multiple sequences”, Biometrika, 97:3 (2010), 631–645 | DOI | MR | Zbl