Inference for clusters of extreme values. (English) Zbl 1065.62091

Ferro, Christopher A. T.; Segers, Johan

J. R. Stat. Soc., Ser. B, Stat. Methodol. 65, No. 2, 545-556 (2003).

Summary: Inference for clusters of extreme values of a time series typically requires the identification of independent clusters of exceedances over a high threshold. The choice of the declustering scheme often has a significant effect on estimates of cluster characteristics. We propose an automatic declustering scheme that is justified by an asymptotic result for the times between threshold exceedances. The scheme relies on the extremal index, which we show may be estimated before declustering, and supports a bootstrap procedure for assessing the variability of estimates.

MSC:

62G32	Statistics of extreme values; tail inference
62M09	Non-Markovian processes: estimation
62E20	Asymptotic distribution theory in statistics

Keywords:

extreme values; interexceedance times; interval estimators; maximum likelihood

References:

[1]	Davison A. C., J. R. Statist. Soc. 52 pp 393– (1990)
[2]	Ferro C. A. T., Technical Report 2002-025 (2002)
[3]	DOI: 10.1016/0304-4149(87)90183-9 · Zbl 0645.60057
[4]	DOI: 10.1016/0304-4149(91)90064-J · Zbl 0722.62021
[5]	Hsing T., Probab. Theory Reltd Flds 78 pp 97– (1988)
[6]	Leadbetter M. R., Z. Wahrsch. Ver. Geb. 65 pp 291– (1983)
[7]	DOI: 10.1016/0378-3758(94)00075-1 · Zbl 0819.60050
[8]	Leadbetter M. R., Extremes and Related Properties of Random Sequences and Processes (1983) · Zbl 0518.60021
[9]	Leadbetter M. R., Technical Report 253 (1989)
[10]	DOI: 10.1016/S0378-4266(99)00077-1
[11]	O’Brien G. L., Ann. Probab. 15 pp 281– (1987)
[12]	Smith R. L., Biometrika 84 pp 249– (1997)
[13]	Smith R. L., J. R. Statist. Soc. 56 pp 515– (1994)
[14]	DOI: 10.1016/S0378-3758(97)00095-5 · Zbl 0953.62089