Prediction Intervals of Future Observations with Parameter Constraints

Abstract

The Prediction of future observations with constraints is a fundamental problem in applied statistics. In this paper, we consider incorporating parameter constraints into the frequentist, Bayesian, fiducial and inferential model (IM) prediction frameworks. As two simple examples, the constrained Gaussian and Poisson models often appear in high energy physics and we use these two models to introduce constrained prediction methods. Since the prediction interval (PI) is a useful tool for predicting future data, our simulation studies show that the PIs of fiducial and IM have better coverage performance than the frequentist and Bayesian PIs. We also discuss the use of the fiducial and IM PIs. Finally, two real examples are used to demonstrate the application of different methods.

Keywords

Constrained statistical inference / Inferential model / Plausibility function / Prediction interval / Coverage probability / 62F30 / 62P35

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Funding

China Postdoctoral Science Foundation(2021M690774)

National Natural Science Foundation of China(11731015)

Natural Science Foundation of Guangdong Province(2019A1515011717)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature