Optimal Nonparametric Multivariate Change Point Detection and Localization

We study the multivariate nonparametric change point detection problem, where data are a sequence of independent $p$ -dimensional random vectors whose distributions piecewise-constant with Lipschitz densities changing at unknown times, called points. quantify size distributional any supremum norm difference between corresponding densities. concerned localization task estimating positions In our analysis, we allow for model parameters to vary total number time points, including minimal spacing consecutive points and magnitude smallest change. provide information-theoretic lower bounds on both rate signal-to-noise ratio required guarantee consistent localization. formulate novel algorithm based kernel density estimation that nearly achieves minimax bound, save possibly logarithm factors. have provided extensive numerical evidence support theoretical findings.