The Projack: A Resampling Approach for Prediction of Ranked Effect Sizes and Estimation of Normal Means

• Activity Number: 642
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Yihui Zhou*+ and Fred Wright
• Companies: University of North Carolina, Chapel Hill and The University of North Carolina

Abstract

The problem of ranked inference arises in a number of settings, for which the investigator wishes to perform parameter inference after ranking a set of m statistics. In contrast to inference for a single hypothesis, the ranking procedure introduces considerable bias. Even for independent z statistics, the problem is nontrivial, and has connections to the classic problem of estimating a multivariate mean vector. We introduce the projack, a resampling-based procedure that provides accurate estimates and coverage intervals of the underlying mean parameter for a set of possibly correlated z statistics. The approach is initially motivated for the setting where original data is available for resampling, a simple extension is applicable when only the vector of z values is available. We illustrate the projack for gene expression data, and for classical datasets used for shrinkage estimation and prediction.