Incorporating Relative Error Criterion to Conformal Prediction for Positive Data

Abstract

Positive data are very common in many scientific fields and applications; for these data, it is known that estimation and inference based on relative error criterion are superior to that of absolute error criterion. In prediction problems, conformal prediction provides a useful framework to construct flexible prediction intervals based on hypothesis testing, which has been actively studied in the past decade. In view of the advantages of the relative error criterion for regression problems with positive responses, in this paper, we combine the relative error criterion (REC) with conformal prediction to develop a novel REC-based predictive inference method to construct prediction intervals for the positive response. The proposed method satisfies the finite sample global coverage guarantee and to some extent achieves the local validity. We conduct extensive simulation studies and two real data analysis to demonstrate the competitiveness of the new proposed method.

Keywords

Conformal prediction / Neural network / Positive responses / Relative error criterion / Regression data

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