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Abstract:
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We propose a class of test statistics for a change point in the mean of high-dimensional independent data. Our test integrates the U-statistic based approach in a recent work by Wang et al. (2019) and the Lq-norm based high-dimensional test in He et al. (2018), and inherits several appealing features such as being tuning parameter free and asymptotic independence for test statistics for differentq?2N. A simple combination of test statistics corresponding to several different q's leads to a test with adaptive power property, that is, it can be powerful against both sparse and dense alternatives. As a natural extension, we combine our tests with wild binary segmentation algorithm to estimate the number and locations of multiple change points. Numerical comparisons using both simulated and real data demonstrate the advantage of our adaptive test and its corresponding estimation method.
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