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- Title
Statistical calibration for infinite many future values in linear regression: simultaneous or pointwise tolerance intervals or what else?
- Authors
Han, Yang; Sun, Yujia; Wang, Lingjiao; Liu, Wei; Bretz, Frank
- Abstract
Statistical calibration using regression is a useful statistical tool with many applications. For confidence sets for x -values associated with infinitely many future y -values, there is a consensus in the statistical literature that the confidence sets constructed should guarantee a key property. While it is well known that the confidence sets based on the simultaneous tolerance intervals (STIs) guarantee this key property conservatively, it is desirable to construct confidence sets that satisfy this property exactly. Also, there is a misconception that the confidence sets based on the pointwise tolerance intervals (PTIs) also guarantee this property. This paper constructs the weighted simultaneous tolerance intervals (WSTIs) so that the confidence sets based on the WSTIs satisfy this property exactly if the future observations have the x -values distributed according to a known specific distribution F (⋅) . Through the lens of the WSTIs, convincing counter examples are also provided to demonstrate that the confidence sets based on the PTIs do not guarantee the key property in general and so should not be used. The WSTIs have been applied to real data examples to show that the WSTIs can produce more accurate calibration intervals than STIs and PTIs.
- Subjects
CALIBRATION; CONFIDENCE
- Publication
Journal of the Royal Statistical Society: Series C (Applied Statistics), 2023, Vol 72, Issue 1, p37
- ISSN
0035-9254
- Publication type
Article
- DOI
10.1093/jrsssc/qlac004