Assessing multivariate nonnormality using univariate distributions

Biometrika

Volumn 86, Issue 1, 1999, Pages 191-202

  Slate, Elizabeth H ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

Bayesian inference; Dynamic graphics; Multivariate likelihood function; Multivariate posterior distribution; Nonnormality; Reparameterisation; Simulated annealing; Tail probability

Indexed keywords

EID: 3042582050     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/86.1.191     Document Type: Article

References (20)

1. ANSCOMBE, F. J. (1964). Normal likelihood functions. Ann. Inst. Statist. Math. 16, 1-19.
2. BATES, D. M. & WATTS, D. G. (1980). Relative curvature measures of nonlinearity (with Discussion). J. R. Statist. Soc. B 42, 1-25.
3. BROOKS, S. P. & MORGAN, B. J. T. (1995). Optimization using simulated annealing. Statistician 44, 241-57.
4. COOK. R. D. & WEISBERG, S. (1982). Residuals and Influence in Regression. London: Chapman and Hall.
5. DICICCIO, T. J., FIELD, C. A. & FRASER, D. A. S. (1990). Approximations of marginal tail probabilities and inference for scalar parameters. Biometrika 77, 77-95.
6. DICICCIO, T. J. & STERN, S. E. (1993). Bartlett adjustments for Bayesian inference. Biometrika 80, 731-40.
7. DRAPER, N. R. & SMITH, H. (1998). Applied Regression Analysis, 3rd ed. New York: Wiley.
8. FEIGL, P. & ZELEN, M. (1965). Estimation of exponential survival probabilities with concomitant information. Biometrics 21, 826-38.
9. GILKS, W. R. & ROBERTS, G. O. (1996). Strategies for improving MCMC. In Markov Chain Monte Carlo in Practice, Ed. W. R. Gilks, S. Richardson and D. J. Spiegelhalter, pp. 89-114. New York: Chapman and Hall.
10. HODGES, J. S. (1987). Assessing the accuracy of normal approximations. J. Am. Statist. Assoc. 82, 149-54.
11. JOHNSON, N. L. & KOTZ, S. (1970). Continuous Univariate Distributions-1. New York: Wiley.
12. KASS, R. E. (1989). The geometry of asymptotic inference (with Discussion). Statist. Sci. 4, 188-234.
13. KASS, R. E. & SLATE, E. H. (1994). Some diagnostics of maximum likelihood and posterior non-normality. Ann. Statist. 22, 668-95.
14. KASS, R. E., TIERNEY, L. & KADANE, J. B. (1989). Approximate methods for assessing influence and sensitivity in Bayesian analysis. Biometrika 76, 663-74.
15. MCCULLAGH, P. (1987). Tensor Methods in Statistics. London: Chapman and Hall.
16. SLATE, E. H. (1994). Parameterizations for natural exponential families with quadratic variance functions. J. Am. Statist. Assoc. 89, 1471-82.
17. SPROTT, D. A. (1973). Normal likelihoods and their relation to large sample theory of estimation. Biometrika 60, 457-65.
18. TIERNEY, L. (1990). Lisp-Stat: An Object-Oriented Environment for Statistical Computing and Dynamic Graphics. New York: Wiley.
19. TIERNEY, L. & KADANE, J. B. (1986). Accurate approximations for posterior moments and marginal densities. J. Am. Statist. Assoc. 81, 82-6.
20. TIERNEY, L., KASS, R. E. & KADANE, J. B. (1989). Approximate marginal densities of nonlinear functions. Biometrika 76, 425-33. Amendment (1991), 78, 233-4.