The Annals of Statistics

Limit theorem for maximum of standardized U-statistics with an application

Lajos Horváth and Qi-Man Shao

Full-text: Open access

Abstract

We show that the maximally selected standardized U-statistic goes in distribution to an infinite sum of weighted chi-square random variables in the degenerate case. The result is applied to the detection of possible changes in the distribution of a sequence observation.

Article information

Source
Ann. Statist., Volume 24, Number 5 (1996), 2266-2279.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362321

Digital Object Identifier
doi:10.1214/aos/1069362321

Mathematical Reviews number (MathSciNet)
MR1421172

Zentralblatt MATH identifier
0903.62044

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62G10: Hypothesis testing 60F05: Central limit and other weak theorems

Keywords
Degenerate $U$-statistic limit distribution standardized statistics change-point analysis

Citation

Horváth, Lajos; Shao, Qi-Man. Limit theorem for maximum of standardized U -statistics with an application. Ann. Statist. 24 (1996), no. 5, 2266--2279. doi:10.1214/aos/1069362321. https://projecteuclid.org/euclid.aos/1069362321


Export citation