On semiparametric pivotal bayesian inference for quantiles |
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Authors: | TB Swartz C Villegas CJ Martinez |
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Institution: | Department of Mathematics and Statistics , Simon Fraser University , Burnaby, British Columbia, V5A 1S6, Canada |
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Abstract: | In semiparametric inference we distinguish between the parameter of interest which may be a location parameter, and a nuisance parameter that determines the remaining shape of the sampling distribution. As was pointed out by Diaconis and Freedman the main problem in semiparametric Bayesian inference is to obtain a consistent posterior distribution for the parameter of interest. The present paper considers a semiparametric Bayesian method based on a pivotal likelihood function. It is shown that when the parameter of interest is the median, this method produces a consistent posterior distribution and is easily implemented, Numerical comparisons with classical methods and with Bayesian methods based on a Dirichlet prior are provided. It is also shown that in the case of symmetric intervals, the classical confidence coefficients have a Bayesian interpretation as the limiting posterior probability of the interval based on the Dirichlet prior with a parameter that converges to zero. |
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Keywords: | pivotal posteriors sign test statistic consistent posteriors Dirichlet process |
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