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A Matching Prior for the Shape Parameter of the Skew‐Normal Distribution
Author(s) -
CABRAS STEFANO,
RACUGNO WALTER,
CASTELLANOS MARÍA EUGENIA,
VENTURA LAURA
Publication year - 2012
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.0775.x
Subject(s) - mathematics , prior probability , nuisance parameter , skew , scale parameter , shape parameter , matching (statistics) , bayesian linear regression , posterior predictive distribution , bayesian probability , computation , distribution (mathematics) , likelihood function , monotone polygon , posterior probability , estimation theory , bayesian inference , algorithm , statistics , computer science , estimator , mathematical analysis , telecommunications , geometry
. This paper deals with the issue of performing a default Bayesian analysis on the shape parameter of the skew‐normal distribution. Our approach is based on a suitable pseudo‐likelihood function and a matching prior distribution for this parameter, when location (or regression) and scale parameters are unknown. This approach is important for both theoretical and practical reasons. From a theoretical perspective, it is shown that the proposed matching prior is proper thus inducing a proper posterior distribution for the shape parameter, also when the likelihood is monotone. From the practical perspective, the proposed approach has the advantages of avoiding the elicitation on the nuisance parameters and the computation of multidimensional integrals.