Speaker
Description
Multiple-use prediction and calibration for all future values play a valuable role in many areas including health and medical research. Simultaneous tolerance bands (STBs) can be used for these purposes. Motivated by real-world problems in health research, this study focuses on the construction of exact STBs for multiple regression over any given rectangular covariate region and for polynomial regression over any given covariate interval.
We first address a key gap in the literature by constructing exact STBs for multiple regression over a given rectangular covariate region. A new simultaneous tolerance band (STB) is also proposed for both multiple and polynomial regression models. Unlike approximate or conservative methods, the exact STB rigorously guarantees the pre-specified confidence level. This new STB is compared systematically with existing approaches under the average shift criterion.
Our numerical results show that the new STB outperforms existing alternatives under the average shift criterion and is thus recommended. We apply the new STB to two critical health applications: predicting blood pressure levels in infants and calibrating gestational ages. By leveraging exact STBs, based on a single training dataset, our method enables precise predictions and calibrations for infinitely many future observations.
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