Asymptotics of Studentized U-type processes for changepoint problems

TL;DR

This paper develops asymptotic approximations for studentized U-type processes under minimal conditions, enabling more robust changepoint detection in sequences without strict moment assumptions.

Contribution

It introduces weighted approximation results for studentized U-processes with symmetric and antisymmetric kernels, relaxing classical moment conditions and applicable to changepoint testing.

Findings

Weighted approximations hold under domain of attraction of the normal law.

Classical second moment condition is relaxed.

Results are applicable for changepoint hypothesis testing.

Abstract

This paper investigates weighted approximations for studentized $U$-statistics type processes, both with symmetric and antisymmetric kernels, only under the assumption that the distribution of the projection variate is in the domain of attraction of the normal law. The classical second moment condition $E|h(X_1,X_2)|^2 < \infty$ is also relaxed in both cases. The results can be used for testing the null assumption of having a random sample versus the alternative that there is a change in distribution in the sequence.