Rubio, F. J. and Steel, Mark F. J. (2011) Inference in two-piece location-scale models with Jeffreys priors. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).

Preview

PDF WRAP_Rubio_11-13w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (405Kb)

Abstract

This paper addresses the use of Jeffreys priors in the context of univariate threeparameter location-scale models, where skewness is introduced by differing scale parameters either side of the location. We focus on various commonly used parameterizations for these models. Jeffreys priors are shown not to allow for posterior inference in the wide and practically relevant class of distributions obtained by skewing scale mixtures of normals. Easily checked conditions under which independence Jeffreys priors can be used for valid inference are derived. We empirically investigate the posterior coverage for a number of Bayesian models, which are also used to conduct inference on real data.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Bayesian statistical decision theory
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2011
Volume:	Vol.2011
Number:	No.13
Number of Pages:	27
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	Arnold, B. C. and Groeneveld, R. A. (1995). Measuring skewness with respect to the mode. The American Statistician 49: 34–38. Arellano-Valle, R. B., G´omez, H. W. and Quintana, F. A. (2005). Statistical inference for a general class of asymmetric distributions. Journal of Statistical Planning and Inference 128: 427–443. Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12: 171-178. Bayes, C. L. and Branco, M. D. (2007). Bayesian inference for the skewness parameter of the scalar skew-normal distribution. Brazilian Journal of Probability and Statistics 21: 141–163. Berger, J. O., Bernardo, J. M. and Sun, D. (2009). The formal definition of reference priors. Annals of Statistics 37: 905–938. Berger, J. O. and Sun, D. (2008). Objective priors for the bivariate normal model.Annals of Statistics 36: 963–982. Chopin, N. and Robert, C. P. (2010). Properties of nested sampling. Biometrika 97: 741–745. Clarke, B. and Barron, A. R. (1994). Jeffreys’ prior is asymptotically least favorable under entropy risk. Journal of Statistical Planning and Inference 41: 37–60. Cox, D. R. and Reid, N. (1987). Orthogonality and approximate conditional inference. Journal of the Royal Statistical Society, Series B 49: 1–39. Fern´andez, C. and Steel, M. F. J. (1998). On Bayesian modeling of fat tails and skewness. Journal of the American Statistical Association 93: 359–371. Fern´andez, C. and Steel, M. F. J. (2000). Bayesian regression analysis with scale mixtures of normals. Econometric Theory 16: 80–101. Fr¨uhwirth-Schnatter, S. (2004). FiniteMixture and Markov SwitchingModels. Springer Series in Statistics: New York. Geweke, J. (1989). Bayesian inference in econometric models using Monte Carlo integration. Econometrica 57: 1317-1339. Gibbons, J. F. and Mylroie, S. (1973). Estimation of impurity profiles in ion-implanted amorphous targets using joined half-Gaussian distributions. Applied Physics Letters 22: 568–569. Jeffreys, H. (1941). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A, 183: 453–461. Jeffreys, H. (1961). Theory of Probability (3rd ed.) Oxford: Clarendon. John, S. (1982). The three-parameter two-piece normal family of distributions and its fitting. Communications in Statistics - Theory and Methods 11: 879-885. Jones, M. C. (2006). A note on rescalings, reparametrizations and classes of distributions. Journal of Statistical Planning and Inference 136: 3730-3733. Jones, M. C. and Anaya-Izquierdo K. (2010). On parameter orthogonality in symmetric and skew models. Journal of Statistical Planning and Inference 141: 758–770. Liseo, B. and Loperfido, N. (2006). A note on reference priors for the scalar skewnormal distribution. Journal of Statistical Planning and Inference 136: 373-389. Mudholkar, G. S. and Hutson, A. D. (2000). The epsilon-skew-normal distribution for analyzing near-normal data. Journal of Statistical Planning and Inference 83: 291– 309. Xu, A. and Tang, Y. (2011). Bayesian analysis of Birnbaum-Saunders distribution with partial information. Computational Statistics and Data Analysis, 55: 2324–2333.
URI:	http://wrap.warwick.ac.uk/id/eprint/35059

Request changes to a record

Actions (login required)

View Item