A matching prior based on the modified profile likelihood for the common mean in multiple log-normal distributions

Yongku Kim (), Woo Dong Lee () and Sang Gil Kang ()
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Yongku Kim: Kyungpook National University
Woo Dong Lee: Daegu Haany University
Sang Gil Kang: Sangji University

Statistical Papers, 2020, vol. 61, issue 2, No 2, 543-573

Abstract: Abstract In this paper, we develop a matching prior for the common mean in several log-normal distributions. For this problem, assigning priors appropriately for the common log-normal mean is challenging owing to the presence of nuisance parameters. Matching priors, which are priors that match the posterior probabilities of certain regions within their frequentist coverage probabilities, are commonly used in this problem. However, a closed form posterior under the derived first order matching prior is not available; further, the second order matching prior is difficult to be derived in this problem. Thus, alternatively, we derive a matching prior based on a modification of the profile likelihood. Simulation studies show that this proposed prior meets the target coverage probabilities very well even for small sample sizes. Finally, we present a real example.

Keywords: Matching prior; Modified profile likelihood; Common log-normal mean (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-017-0950-4

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