A1605
Title: High-dimensional change point detection with missing values
Authors: Abolfazl Safikhani - George Mason University (United States) [presenting]
Abstract: Assuming fixed model parameters over a relatively large time interval is unrealistic due to possible external shocks to the dynamics of the data generating process. A more realistic assumption is to let parameters behave in a piecewise constant manner, where time points with jumps in model parameters are called change points. A change point detection problem in a high-dimensional mean shift model with missing values is considered. The presence of missing values among observations further complicates the detection problem due to possible loss of information before and after a change point. A four-step algorithm is designed to tackle this problem. First, observations are split into blocks of a certain size and a regularized estimator is defined to perform parameter estimation while missing values are imputed properly. This step is followed by thresholding and re-imputation to fine-tune the estimation results due to the occurrence of misspecification in the first step. Finally, an exhaustive search is performed to locate the change points. Theoretical properties of the proposed algorithm are established, including the consistency of estimating both the unknown number and the location of change points under mild conditions. Furthermore, the effectiveness of the developed detection algorithm is confirmed empirically through comparison with competing methods as well as through various synthetic data and two real data examples.
