A1089
Title: Multiple change-points for offline functional data: Estimation and testing
Authors: Anirvan Chakraborty - IISER Kolkata (India) [presenting]
Sourav Chakrabarty - ISI Kolkata (India)
Shyamal Krishna De - ISI Kolkata (India)
Abstract: Some novel procedures are presented for detecting the number, say K, of changepoints and their locations for offline functional data when K is unknown as well as when lower/upper bounds are provided for it. These algorithms utilize an intriguing property of the maximum mean discrepancy (MMD) metric between two distributions. This property is exploited to develop the algorithms using a binary splitting technique to recursively partition the dataset into groups based on a weighted MMD measure. An exact permutation testing step is built-in to assess the statistical significance of any detected changepoint in case K is unknown. When some lower/upper bound for K is provided, a merging step is instead used to merge consecutive splits that are considered similar based on the weighted MMD measure. Theoretical investigations demonstrate strong consistency of the estimated changepoints in both single and multiple changepoint situations. Moreover, the consistency of the permutation test used is established for the at-most-one-changepoint (AMOC) setup. When specific information about K is available, the algorithm exhibits a desirable order-preserving property. Extensive simulated and real data analyses demonstrate the superiority of the suggested algorithms for a variety of structural changepoints compared to some of the existing techniques for functional data.
