Lingzhou Xue - Seminar Series

November 17, 2017 -
2:00pm to 3:00pm

Lingzhou Xue, PhD

Innovated Power Enhancement Tests for Complex and High Dimensional Data

Abstract: In the current literature, two sets of test statistics are commonly used for high-dimensional tests: 1) using extreme-value form statistics to test against sparse alternatives, and 2) using quadratic form statistics to test against dense alternatives. However, quadratic form statistics suffer from low power against sparse alternatives, and extreme-value form statistics suffer from low power against dense alternatives with small disturbances and may have size distortions due to its slow convergence. For real-world applications, it is important to derive powerful testing procedures against more general alternatives. Based on their joint limiting laws, we introduce a new general power enhancement testing procedure to boost the power against more general alternatives and retain the correct asymptotic size. Under the high-dimensional setting, we derive the closed-form limiting null distributions, and obtain their explicit rates of uniform convergence. The proposed power enhancement test is demonstrated in various parametric and nonparametric tests for high-dimensional means, banded covariances, spiked covariances, and so on. We demonstrate the finite-sample performance of our proposed testing procedures in both simulation studies and real applications.

Location and Address

1811 Wesley W. Posvar Hall

230 South Bouquet St.

Pittsburgh, PA 15213