Prediction with Confidence: A Frequentist Predictive Distribution Function and a Unifying Framework

• Activity Number: 322
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Min-ge Xie*+
• Companies: Rutgers University
• Keywords: confidence distribution ; prediction ; confidence level ; frequentist ; distributional inference

Abstract

In this talk, we develop a new and general framework for prediction, in which a prediction is presented in the form of a distribution function, called predictive distribution function. This predictive distribution function, developed based on confidence distributions, has a clear frequentist probability interpretation and can provide meaningful answers for all sorts of questions related to prediction. It can also serve as a unifying point for existing procedures of predictive inference in Bayesian, fiducial and frequentist paradigms. A simple yet broadly applicable algorithm by Monte-Carlo or bootstrapping is also proposed. An application on extreme value data analysis is used to illustrate the methodology and to provide a prediction of the performances of gold medalists in the next Olympic Games.