Title: Two-sample mean test for high-dimensional time series
Authors: Shuyi Zhang - East China Normal University (China) [presenting]
Song Xi Chen - Peking University (China)
Yumou Qiu - Iowa State University (United States)
Abstract: Two population means are tested with high-dimensional temporally dependent data. To eliminate the bias caused by the temporal dependence among the time-series observations, a band-excluded U-statistic (BEU) is proposed to estimate the squared Euclidean distance between the two means, which excludes cross-products of data vectors between temporally close time points. The asymptotic normality of the BEU statistic is derived under the high dimensional setting with ``spatial'' (column-wise) and temporal dependence. An estimator built on the kernel smoothing over cross-time covariances is developed to estimate the variance of the BEU-statistic, which facilitates a test procedure based on the BEU statistic. The proposed test is nonparametric and adaptive to a wide range of dependence and dimensionality, and has attractive power properties relative to a self-normalized test. Numerical analysis and a real data analysis on a meteorological data-set were conducted to demonstrate the performance and utility of the proposed test.