Prediction with confidence-A general framework for predictive inference

This paper proposes a 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 is well suited for the notion of confidence subscribed in the frequentist interpretation, and it can provide meaningful answers for questions related to prediction. A general approach under this framework is formulated and illustrated by using the so-called confidence distributions (CDs). This CD-based prediction approach inherits many desirable properties of CD, including its capacity for serving as a common platform for connecting and unifying the existing procedures of predictive inference in Bayesian, fiducial and frequentist paradigms. The theory underlying the CD-based predictive distribution is developed and some related efficiency and optimality issues are addressed. Moreover, a simple yet broadly applicable Monte Carlo algorithm is proposed for the implementation of the proposed approach. This concrete algorithm together with the proposed definition and associated theoretical development produce a comprehensive statistical inference framework for prediction. Finally, the approach is applied to simulation studies, and a real project on predicting the incoming volume of application submissions to a government agency. The latter shows the applicability of the proposed approach to dependence data settings.