Adaptive Inference for Change Points in High-Dimensional Data

In this article, we propose a class of test statistics for change point in the mean high-dimensional independent data. Our integrates U-statistic based approach recent work by Wang et al. and Lq-norm He al., inherits several appealing features such as being tuning parameter free asymptotic independence corresponding to even q’s. A simple combination different q’s leads with adaptive power property, that is, it can be powerful against both sparse dense alternatives. On estimation front, obtain convergence rate maximizer our statistic standardized sample size when there is one change-point q = 2, combine tests wild binary segmentation algorithm estimate number locations are multiple change-points. Numerical comparisons using simulated real data demonstrate advantage its method.