Two-sided Bayesian and frequentist tolerance intervals: general asymptotic results with applications

Abstract

It is well known that that the construction of two-sided tolerance intervals is far more challenging than that of their one-sided counterparts. In a general framework of parametric models, we derive asymptotic results leading to explicit formulae for two-sided Bayesian and frequentist tolerance intervals. In the process, probability matching priors for such intervals are characterized and their role in finding frequentist tolerance intervals via a Bayesian route is indicated. Furthermore, in situations where matching priors are hard to obtain, we develop purely frequentist tolerance intervals as well. The findings are applied to real data. Simulation studies are seen to lend support to the asymptotic results in finite samples.

Keywords:

• higher order
• Jeffreys’ prior
• probability matching prior
• shrinkage argument

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ERRATUM

Acknowledgements

We thank the referees for constructive suggestions. The work of Rahul Mukerjee was supported by the J.C. Bose National Fellowship of the Government of India and a grant from the Indian Institute of Management Calcutta. The work of S.H. Ong was supported by the Fundamental Research Grant FRGS/1-2010/FP003/2010A.

Notes

This version has been corrected. Please see Erratum (10.1080/02331888.2013.785099).