Predictive sets with approximate frequentist and Bayesian validity for arbitrary priors

Abstract

With a view to predicting a scalar-valued future observation on the basis of past observations, we explore predictive sets having frequentist as well as Bayesian validity for arbitrary priors in a higher-order asymptotic sense. It is found that a connection with locally unbiased tests is useful for this purpose. Illustrative examples are given. Computation and simulation studies lend support to our asymptotic results in finite samples. The issue of expected lengths of our predictive sets is also discussed.

Keywords:

• higher-order asymptotics
• locally unbiased test
• shrinkage argument

Acknowledgements

We thank the associate editor and a referee for very useful, constructive suggestions.

Additional information

Funding

This work was supported by research grant, starting 2012, from Chosun University.