Single Change-Point Detection via Energy Distance with Application to Genomic Data

TL;DR

This paper introduces a nonparametric energy distance-based method for single change-point detection in sequences, demonstrating robustness and applicability to genomic data.

Contribution

It develops a new energy distance-based test with proven asymptotic properties and extends it to multiple change points with binary segmentation.

Findings

The test statistic converges to a standard normal distribution under the null hypothesis.

Permutation calibration ensures valid type I error control.

The method shows superior robustness across various error distributions.

Abstract

In this paper, we develop and analyze a nonparametric procedure for detecting a single change point in sequences of independent observations using energy distance. The asymptotic properties of the test statistic are derived under both null and alternative hypotheses. Under the null hypothesis, for any fixed candidate split point, the standardized statistic $\mathcal{Z}_{n,k}$ converges to a standard normal limit. For global detection, we use the scan statistic $T_n=\max_{k\in K_\eta}|\mathcal{Z}_{n,k}|$ and calibrate critical values using a permutation test, which yields valid type I error control under exchangeability. The simulation study shows that the proposed method demonstrates much better robustness across various error distributions. To handle multiple change points in practical applications, the method is combined with a binary segmentation approach. The breast cancer cell line (MDA157) from cDNA microarray CGH data is used to illustrate the detection and estimation capabilities of the proposed method for genomic sequences.