Multiple-use calibration for all future values and exact two-sided simultaneous tolerance intervals in linear regression

Abstract

Multiple-use calibration using regression is an important statistical tool. Confidence sets for the x-values associated with all future y-values should guarantee a key property, which can be satisfied by simultaneous tolerance intervals (STI’s), and so multiple-use calibration requires the construction of STI’s. In this paper, exact two-sided STI’s have been constructed for polynomial regression over any given covariate interval. There is a misconception that two-sided pointwise tolerance intervals (PTI’s) can be employed for multiple-use calibration. This paper shows that the confidence sets based on the two-sided PTI’s do not satisfy the key property and so should not be used. Real-world data examples are given in this paper for illustration.