Confidence Distribution, Data Depth, and Combination of Nonparametric Inference

• Activity Number: 147
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Dungang Liu and Regina Y Liu*+ and Minge Xie
• Companies: Rutgers University and Rutgers University and Rutgers University
• Keywords: confidence distribution ; data depth ; combination inference ; nonparametric inference

Abstract

We apply the concepts of confidence distribution (CD) and data depth to develop a new combined inference for multiple nonparametric studies of a common hypothesis. A CD can be viewed as a "distribution estimator" of the parameter of interest, finite or infinite dimensional. Examples of CDs include Efron's bootstrap distribution and Fraser's p-value function. Although a natural frequentist concept, CD also has natural links to Bayesian inference and Fisher's fiducial arguments. CD can be an effective tool for statistical inference. We propose a new approach to combining test results from multiple studies on a common multivariate hypothesis. Specifically, in each study we apply data depth and bootstraps to obtain a p-value function for the common hypothesis. The p-value functions are then combined under the framework of combining CDs. This approach allows resampling directly from data, rather than from the estimated null population distribution. Moreover, it obtains test results directly, bypassing the tasks of constructing an explicit test statistic and establishing its corresponding sampling distribution. We illustrate the approach using simulation data and flight data from FAA.