U-Statistics in Sequential Tests and Change Detection

Abstract

Research on U-statistics within the general framework of sequential and change-point literature is surveyed. Some recent developments are discussed and extended. New sequential testing strategies based on Wiener process approximations are proposed, and empirical studies explore the finite sample performance of these tests. It allows users to choose one that is appropriate for their application.

Key Words:

• U-Statistic
• Change-point detection
• Sequential tests
• Stochastic processes
• Strong approximations

AMS Subject Classifications:

• Primary 62G20
• Secondary 60F05, 62G10

Acknowledgments

The author wishes to thank the referees for their careful reading of the manuscript, and for their helpful suggestions. The research is supported in part by a NSERC Canada operating grant.

Notes

Recommended by M. Baron.