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Abstract:
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We propose a general framework for prediction, in which a prediction is presented in the form of a predictive distribution function. This predictive distribution function is well suited for the notion of confidence used in frequentist interpretation, and can provide meaningful answers for all questions related to prediction. A specific approach under this general prediction framework is formulated and illustrated by using confidence distributions (CDs). This CD-based prediction approach inherits many desirable properties of CD, including its capacity in 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 a related efficiency issue is also addressed. Moreover, a simple yet broadly applicable Monte-Carlo algorithm is proposed for the implementation of the proposed approach, which, together with the proposed definition and associate theoretical development, produces a comprehensive statistical inference framework for prediction.
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