Juárez, Miguel A. (2005) Normal correlation : an objective Bayesian approach. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.

Preview

PDF WRAP_Juarez-05-15wv1.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (461Kb)

Abstract

In this paper we give a decision-theoretic oriented, objective Bayesian answer to the problems of point estimating and sharp hypothesis testing about the correlation coefficient of a bivariate Normal population. Under this view both problems are deemed closely related and thus a coherent answer is developed. Comparisons with frequentist results are given and an alternative interpretation of the maximum likelihood estimator is found.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Fix-point estimation, Statistical hypothesis testing, Correlation (Statistics)
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2005
Volume:	Vol.2005
Number:	No.15
Number of Pages:	15
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
References:	Bartlett, M. (1957). A comment on D. V. Lindley’s statistical paradox, Biometrika, 44, 533–534. Bayarri, M. J. (1981). Inferencia bayesiana sobre el coeficiente de correlación en una población normal bivariante, Trabajos de Estadística e Investigación Operativa, 32 (3), 18–31. Berger, J. O. and Bernardo, J. M. (1992). On the development of reference priors, Bayesian Statistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.), Oxford: University Press, pp. 35–60. Berger, J. O. and Pericchi, L. R. (2001). Objective Bayesian methods for model selection: Introduction and comparison, Model Selection, Lecture Notes, vol. 38 (P. Lahiri, ed.), Institute of Mathematical Statistics, pp. 135–207. (with discussion). Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference, J. Roy. Statist. Soc. B, 41 (2), 113–147. Bernardo, J. M. and Juárez, M. A. (2003). Intrinsic estimation, Bayesian Statistics 7 (J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West, eds.), Oxford: University Press, pp. 465–475. Bernardo, J. M. and Rueda, R. (2002). Bayesian hypothesis testing: A reference approach, International Statistical Review, 70, 351–372. Bernardo, J. M. and Smith, A. F. (1994). Bayesian Theory, Chichester: John Wiley. Fisher, R. A. (1915). Frequency distribution of the values of the correlation coefficient in samples of an indefinitely large population, Biometrika, 10, 507–521. Gutierrez-Peña, E. (1992). Expected logarithmic divergence for exponential families, Bayesian Statistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.), Oxford university press, pp. 669–674. Hand, D. J., Daly, F., Lunn, A. D., McConway, K. J. and Ostrowski, E. (1994). A Handbook of small data sets, London: Chapman and Hall. Jeffreys, H. (1961). Theory of Probability, Oxford: University Press, third ed. Juárez, M. A. (2004). Objective Bayes methods for estimation and hypothesis testing, Unpublished PhD thesis, Universitat de Valencia. Lehmann, E. L. (1986). Testing Statistical Hypotheses, New York: John Wiley, second ed. Lindley, D. V. (1957). A statistical paradox, Biometrika, 44, 187–192. Lindley, D. V. (1972). Introduction to Probability and Statistics from a Bayesian Viewpoint, Part 2, Cambridge: Cambridge University Press. O’Hagan, A. (1997). Properties of intrinsic and fractional Bayes factors, Test, 6, 101–118. Pearson, E. S. and Kendall, M. G. (1970). Studies in the History of Statistics and Probability, London: Griffin. Pearson, K. and Lee, A. (1903). On the laws of inheritance in Man: I. Inheritance of Physical Characters, Biometrika, 2, 357–462. Robert, C. P. (1996). Intrinsic losses, Theory and Decisions, 40, 191–214. Robert, C. P. and Caron, N. (1996). Noninformative Bayesian testing and neutral Bayes factors, Test, 5, 411–437.
URI:	http://wrap.warwick.ac.uk/id/eprint/35589

Request changes to a record

Actions (login required)

View Item