SCHOOL OF STATISTICS

and

THE COLLEGE OF LIBERAL ARTS

UNIVERSITY OF MINNESOTA

BUEHLER-MARTIN DISTINGUISHED LECTURER SERIES

April 19, 20 and 21, 2011

Established by Mr. and Mrs. Thomas Martin

in Memory of

Robert J. Buehler, Professor of Statistics (1963-1988)

Jianqing Fan

Department of Operation Research and Financial Engineering

Princeton University

Control of the False Discovery Rate Under Arbitrary Covariance Dependence

Thursday, April 21, 2011 3:30 PM

Ford Hall 115

(Refreshments: 3:00 PM, Ford Hall 300)

Multiple hypothesis testing is a fundamental problem in high dimensional inference, with wide applications in many scientific fields. In genome-wide association studies, tens of thousands of tests are performed simultaneously to find if any genes are associated with some traits and those tests are correlated. When test statistics are correlated, false discovery control becomes very challenging under arbitrary dependence. In the current paper, we propose a new methodology based on principal factor approximation, which successfully substracts the common dependence and weakens significantly the correlation structure, to deal with an arbitrary dependence structure. We derive the theoretical distribution for false discovery proportion (FDP) in large scale multiple testing when a common threshold is used and provide a consistent FDP. This result has important applications in controlling FDR and FDP. Our estimate of FDP compares favorably with Efron (2007)'s approach, as demonstrated by in the simulated examples. Our approach is further illustrated by some real data applications.

(Joint work with Xu Han and Weijie Gu)