A0852
Title: Prediction and calibration for all future values: Simultaneous tolerance regions for multivariate regression
Authors: Lingjiao Wang - University of Manchester (United Kingdom) [presenting]
Yang Han - University of Manchester (United Kingdom)
Wei Liu - University of Southampton (United Kingdom)
Frank Bretz - Novartis Pharma AG (Switzerland)
Abstract: Multiple-use prediction and calibration for all future values play a valuable role in many fields, including industry, sports, health and medical research. Simultaneous tolerance regions (STRs) can be used for this purpose in multivariate regression, but no construction methods are currently available in the literature. The first aim is to fill the gap by constructing STRs and providing a solution to multiple-use prediction and calibration problems. We also develop weighted simultaneous tolerance regions (WSTRs), showing that confidence sets based on WSTRs can exactly satisfy the key property for multiple-use calibration. Through the lens of WSTRs, we address the misconception that the confidence sets derived from pointwise tolerance regions can guarantee the key property. Several methods are proposed for computing the critical constants for STRs and WSTRs. Simulation studies are conducted to compare these methods in terms of accuracy and computational cost. Real-data examples are provided for illustration.
