Projection Test for High-Dimensional Mean with Optimal Direction

• Activity Number: 504
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Yuan Huang* and Runze Li
• Companies: Penn State and Penn State
• Keywords: PROJECTION TEST ; HIGH-DIMENSIONAL MEAN ; OPTIMAL DIRECTION

Abstract

High-dimensional data are generated by modern technologies at an unprecedented speed and stimulate active research in developing new estimation and inference methodologies. Hypothesis testing for mean vectors has received considerable attention in recent literature. Projection based tests produce linear scores on a reduced dimension such that the classical tests are applicable. Despite the advantage of obtaining exact test, current studies provide no clue for designing projection to achieve high power. In this talk, we propose a novel projection test for high-dimensional one-sample mean problem, which tests H0 : µ = µ0 against H1 : µ != µ0 for a random sample of size N from multivariate normal distribution N(µ, ?) under dimension p > N. Our power-maximization framework is fundamentally different from existing methods. Under this framework, our approach is capable of maximally retaining the useful information and filtering those of little value. A computationally efficient algorithm is proposed for implementation.