Minimum-volume confidence sets for normal linear regression models

摘要

In this article, we establish the minimum-volume confidence sets for normal linear regression models, extending the results in Zhang [Minimum volume confidence sets for parameters of normal distributions. Adv Stat Anal. 2017;101:309-320] on building the minimum-volume confidence sets for parameters of normal distributions. Compared with classical confidence sets, the proposed optimal confidence set is proved to have the smallest volume, for whatever confidence level, sample size and sample data.