Sequential Multiple Testing for Variable Selection in High-Dimensional Linear Model

• Activity Number: 117
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Xinping Cui* and Hailu Chen
• Companies: University of California at Riverside and University of California at Riverside
• Keywords: Covariance test ; False Discovery Rate ; LASSO ; Multiple Hypothesis Testing ; Sequential Multiple Testing ; Ordered Hypothesis

Abstract

Covariance test (Lockhart et al. 2014) provided p-values for all variables that enter into a linear model sequentially along a lasso solution path. Using these p-values to select a model with inferential guarantees is equivalent to multiple hypothesis testing setting where the hypotheses are ordered. In this paper, we proposed a sequential multiple hypothesis testing framework, which considers multiple testing within each step and across all steps along the lasso solution path. Under this framework, we designed stepwise p-values and applied Benjamini-Liu (BL, 1999) step down procedure. We compare it with the Single Step-Down method and ForwardStop and StrongStop procedures. Simulation studies show that our proposed procedure has higher power with FDR controlled at the desired level, especially for large scale and high-dimensional data. Diabetes study and framingham heart study examples are also presented.