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A Bayesian Test For The Mean Of The Power Exponential Distribution

Gómez Villegas, Miguel Ángel and Portela García-Miguel, Javier and Sanz San Miguel, Luis (2008) A Bayesian Test For The Mean Of The Power Exponential Distribution. Communications in statistics. Theory and methods, 37 (18). pp. 2865-2876. ISSN 0361-0926

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Abstract

In this article, we deal with the problem of testing a point null hypothesis for the mean of a multivariate power exponential distribution. We study the conditions under which Bayesian and frequentist approaches can match. In this comparison it is observed that the tails of the model are the key to explain the reconciliability or irreconciliability between the two approaches.


Item Type:Article
Uncontrolled Keywords:Mixed prior distributions; Multivariate point null hypothesis; Posterior probability; Power exponential distribution; p-value; Robust Bayesian analysis.
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:15906
References:

Anderson, T. W. (1955). The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6:170–176.

Basu, S., Miccheli, C. A., Olsen, P. (2001). Power exponential densities for the training and classification of acoustic feature vectors in speech recognition. J. Computat. Graphic. Statist. 10(1):158–184.

Bernardo, J. M., Smith, A. F. M. (1994). Bayesian Theory. Chichester: Wiley.

Casella, G., Berger, R. L. (1987). Reconciling Bayesian and frequentist evidence in the onesided testing problem, (with discussions). J. Amer. Statist. Assoc. 82:106–135.

Crowder, M. J., Hand, D. J. (1990). Analysis of Repeated Measures. London: Chapman and Hall.

Fang, K., Zhang, Y. (1990). Generalized Multivariate Analysis. Beijing: Springer-Verlag.

Gómez–Villegas, M. A., Gómez, E. (1992). Bayes factor in testing precise hypotheses. Commun. Statist. Theor. Meth. 21:1707–1715.

Gómez, E., Gómez–Villegas, M. A., Marín, J. M. (1998). A multivariate generalization of the power exponential family of distributions. Commun. Statist. Theor. Meth. 27:589–600.

Gómez, E., Gómez–Villegas, M. A., Marín, J. M. (2002). Continuous elliptical and exponential power linear dynamic models. J. Multivariate Anal. 83:22–36.

Gómez–Villegas, M. A., Maín, P., Sanz, L. (2002). A suitable Bayesian approach in testing point null hypothesis: some examples revisited. Commun. Statist. Theor. Meth. 31:201–217.

Gómez–Villegas, M. A., Maín, P., Navarro, H., Sanz, L. (2004). Asymptotic relationships between posterior probabilities and p-values using the hazard rate. Statist. Probab. Lett. 66:59–66.

Gómez–Villegas, M. A., Maín, P., Sanz, L. (2008). A Bayesian analysis for the multivariate point null testing problem. Submitted.

Gómez–Villegas, M. A., Sanz, L. (1998). Reconciling Bayesian and frequentist evidence in the point null testing problem. Test 7:207–216.

Gómez–Villegas, M. A., Sanz, L. (2000). -contaminated priors in testing point null hypothesis: a procedure to determine the prior probability. Statist. Probab. Lett. 47:53–60.

Jensen, D. R., Good, I. J. (1983). A representation for ellipsoidal distributions. Siam J. Appl. Math. 43:1194–1200.

Lindsey, J. K. (1999). Multivariate elliptically–contoured distributions for repeated measurements. Biometrics 55:1277–1280.

Lindsey, J. K., Lindsey, P. J. (2006). Multivariate distributions with correlation matrices for repeated measurements. Computat. Statist. Data Anal. 50:720–732.

Lizee, J., Plunkett, T. (2002). Archaeological sampling strategies. http://Archnet.asu.edu.

Oh, M. S. (1998). A Bayes test for simple versus one-sided hypothesis on the mean vector of a multivariate normal distribution. Commun. Statist. Theor. Meth. 27:2371–2389.

Oh, H. S., DasGupta, A. (1999). Comparison of the p-value and posterior probability. J. Statist. Plann. Infer. 76:93–107.

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Last Modified:06 Feb 2014 10:34

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