Simultaneous Two-Sided Tolerance Intervals for a Univariate Linear Regression Model

Abstract

In this article we deal with simultaneous two-sided tolerance intervals for a univariate linear regression model with independent normally distributed errors. We present a method for determining the intervals derived by the general confidence-set approach (GCSA), i.e. the intervals are constructed based on a specified confidence set for unknown parameters of the model. The confidence set used in the new method is formed based on a suggested hypothesis test about all parameters of the model. The simultaneous two-sided tolerance intervals determined by the presented method are found to be efficient and fast to compute based on a preliminary numerical comparison of all the existing methods based on GCSA.

Keywords:

• Linear regression model
• Simultaneous two-sided tolerance interval
• Simultaneous tolerance factor

Mathematics Subject Classification:

• 62F25
• 62J05

Acknowledgments

The author gratefully acknowledges the support of the Operational Program Education for Competitiveness – European Social Fund (project CZ.1.07/2.3.00/ 30.0041) of the Ministry of Education, Youth and Sports of the Czech Republic. The author also acknowledges the support of the Slovak Research and Development Agency (APVV grant 0096-10/STATGUM), and by the Scientific Grant Agency of the Slovak Republic (VEGA grants 2/0038/12 and 2/0043/13).