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Abstract:
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We study the maximum score statistic to detect and estimate local signals in the form of change-points in the level, slope, or other property of a sequence of Gaussian random fields, and to segment the sequence when there appear to be multiple changes. Signals can be define nonparametrically as collections of non-zero observations, perhaps supplemented by sparsity requirements, or by clusters of points of fixed shape, but variable size around specific locations. We find that when there are change-points, natural estimators of variances and auto-correlations can be upwardly biased, resulting in a sometimes serious loss of power. Applications to copy number variations, time series of temperature anomalies, atmospheric CO2 levels, COVID-19 incidence, excess deaths during the COVID-19 pandemic illustrate the general theory.
Various aspects of this research involve contributions from Nancy Zhang, Benny Yakir, Yao Xie, and Xiao Fang.
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