Nonparametric maximum likelihood approach to multiple change-point problems

TL;DR

This paper introduces a nonparametric maximum likelihood method for detecting multiple change-points in data sequences without prior knowledge of their number, applicable to any distribution changes, with proven consistency and efficient computation.

Contribution

It develops a novel nonparametric approach that estimates multiple change-points using likelihood and BIC, without parametric assumptions, and demonstrates its theoretical and practical effectiveness.

Findings

Method accurately detects multiple change-points in simulations.

Proposed approach is computationally efficient and consistent.

Effective prescreening improves detection performance.

Abstract

In multiple change-point problems, different data segments often follow different distributions, for which the changes may occur in the mean, scale or the entire distribution from one segment to another. Without the need to know the number of change-points in advance, we propose a nonparametric maximum likelihood approach to detecting multiple change-points. Our method does not impose any parametric assumption on the underlying distributions of the data sequence, which is thus suitable for detection of any changes in the distributions. The number of change-points is determined by the Bayesian information criterion and the locations of the change-points can be estimated via the dynamic programming algorithm and the use of the intrinsic order structure of the likelihood function. Under some mild conditions, we show that the new method provides consistent estimation with an optimal rate. We also suggest a prescreening procedure to exclude most of the irrelevant points prior to the implementation of the nonparametric likelihood method. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of estimation accuracy and computation time.