Title :

Testing mean changes by maximal ratio statistics

Author(s) :

Gudan, Jovita [Auteur correspondant]
Vilnius University [Vilnius]
Račkauskas, Alfredas [Auteur]
Vilnius University [Vilnius]
Suquet, Charles [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Extremes

Pages :

257–298

Publisher :

Springer Verlag (Germany)

Publication date :

2022

ISSN :

1386-1999

English keyword(s) :

change-point detection
changed segment in the mean
epidemic change
Hölder norm statistics
regularly varying random variables
scan statistics

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]

English abstract : [en]

We propose a new test statistic MRγ,n for detecting a changed segment in the mean, at unknown dates, in a regularly varying sample. Our model supports several alternatives of shifts in the mean, including one changepoint, ...
Show more >We propose a new test statistic MRγ,n for detecting a changed segment in the mean, at unknown dates, in a regularly varying sample. Our model supports several alternatives of shifts in the mean, including one changepoint, constant, epidemic and linear form of a change. Our aim is to detect a short length changed segment `∗, assuming `∗/n to be small as the sample size n is large. MRγ,n is built by taking maximal ratios of weighted moving sums statistics of four sub-samples. An important feature of MRγ,n is to be scale free. We obtain the limiting distribution of ratio statistics under the null hypothesis as well as their consistency under the alternative. These results are extended from i.i.d. samples under H0 to some dependent samples. To supplement theoretical results, empirical illustrations are provided by generating samples from symmetrized Pareto and Log-Gamma distributionsShow less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL