Topic：A Neighborhood-Assisted Hotelling's t-Test for High-Dimensional Means
Speaker：Prof. Y.M. Qiu (University of Nebraska Lincoln)
Time：2017-10-13 (Friday) 9:30
Abstarct: This talk aims to revive the classical Hotelling's t-test in the “large p, small n” paradigm. A Neighborhood-Assisted Hotelling's t-statistic is proposed to replace the inverse of sample covariance matrix in the classical Hotelling's statistic with a regularized covariance estimator. Utilizing a regression model, we establish its asymptotic normality under mild conditions. We show that the proposed test is able to match the performance of the population Hotelling's t-test with the known population covariance under certain conditions, and thus possesses certain optimality. Moreover, the test has the ability to attain its best power possible by adjusting a neighborhood size to unknown structures of population mean and covariance matrix. An optimal neighborhood size selection procedure is proposed to maximize the power of the proposed test via maximizing the signal-to-noise ratio. Simulation experiments and case studies are given to demonstrate the empirical performance of the proposed test.