Noninformative Priors for the Difference of Two Quantiles in Exponential Models

- Journal title : Communications for Statistical Applications and Methods
- Volume 14, Issue 2, 2007, pp.431-442
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2007.14.2.431

Title & Authors

Noninformative Priors for the Difference of Two Quantiles in Exponential Models

Kang, Sang-Gil; Kim, Dal-Ho; Lee, Woo-Dong;

Kang, Sang-Gil; Kim, Dal-Ho; Lee, Woo-Dong;

Abstract

In this paper, we develop the noninformative priors when the parameter of interest is the difference between quantiles of two exponential distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that Jeffreys` prior does not satisfy the first order matching criterion. The Bayesian credible intervals based on the first order probability matching prior meet the frequentist target coverage probabilities much better than the frequentist intervals of Jeffreys` prior. Some simulation and real example will be given.

Keywords

Difference of two quantiles;exponential models;probability matching prior;

Language

English

References

1.

Albers, W. and Lohnberg, P. (1984). An approximate confidence interval for the difference between quantiles in a bio-medical problem. Statistica Neerlandica, 38, 20-22

2.

Barlow, R. E. and Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Reinhart and Winston, New York

3.

Berger, J. O. and Bernardo, J. M. (1989). Estimating a product of means: Bayesian analysis with reference priors. Journal of the American Statistical Association, 84, 200-207

4.

Berger, J. O. and Bernardo, J. M. (1992a). Reference priors in a variance components problem. Bayesian Analysis in Statistics and Econometrics (P. Goel and N. S. Iyengar eds.), 177-194, Springer-Verlag, New York

5.

Berger, J. O. and Bernardo, J. M. (1992b). On the development of reference priors (with discussion). Bayesian Statistics IV (J. M. Bernardo, et. at. eds.), 35-60, Oxford University Press, Oxford

6.

Bernardo, J. M. (1979). Reference posterior distributions for Bayesian inference (with discussion). Journal of the Royal Statistical Society, Ser. B, 41, 113-147

7.

Bristol, D. R. (1990). Distribution-free confidence intervals for the difference between quantiles. Statistica Neerlandica, 44, 87-90

8.

Cox, D. R. and Reid, N. (1987). Orthogonal parameters and approximate conditional inference (with discussion). Journal of Royal Statistical Society, Ser. B, 49, 1-39

9.

Datta, G. S. and Ghosh, J. K. (1995a). On priors providing frequentist validity for Bayesian inference. Biometrika, 82, 37-45

10.

Datta, G. S. and Ghosh, M. (1995b). Some remarks on noninformative priors. Journal of the American Statistical Association, 90, 1357-1363

11.

Datta, G. S. and Ghosh, M. (1996). On the invariance of noninformative priors. The Annal of Statistics, 24, 141-159

12.

Davis, D. J. (1952). An analysis of some failure data. Journal of the American Statistical Association, 47, 113-150

13.

DiCiccio, T. J. and Stern, S. E. (1994). Frequentist and Bayesian Bartlett correction of test statistics based on adjusted profile likelihood. Journal of the Royal Statistical Society, Ser. B, 56, 397-408

14.

Epstein, B. and Sobel, M. (1953). Life testing. Journal of the American Statistical Association, 48, 486-502

15.

Ghosh, J. K. and Mukerjee, R. (1992). Noninformative priors (with discussion). Bayesian Statistics IV (J. M. Bernardo, et. al. eds.), 195-210, Oxford University Press, Oxford

16.

Guo, H. and Krishnamoorthy, K. (2005). Comparison between two quantiles: the normal and exponential cases. Communications in Statistics: Simulation and Computation, 34, 243-252

17.

Huang, L. F. and Johnson, R. A. (2006). Confidence regions for the ratio of percentiles. Statistics & Probability Letters, 76, 384-392

18.

Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. John Wiley & Sons, Hoboken, New Jersey

19.

Mukerjee, R. and Dey, D. K. (1993). Frequentist validity of posterior quantiles in the presence of a nuisance parameter: higher order asymptotics. Biometrika, 80, 499-505

20.

Mukerjee, R. and Ghosh, M. (1997). Second-order probability matching priors. Biometrika, 84, 970-975

21.

Proschan, F. (1963). Theoretical explanation of observed decreasing failure rate. Technometrics, 5, 375-383

22.

Stein, C. M. (1985). On the coverage probability of confidence sets based on a prior distribution. Sequential Methods in Statistics, Banach Center Publications, 16, 485-514

24.

Welch, B. L. and Peers, H. W. (1963). On formulae for confidence points based on integrals of weighted likelihoods. Journal of the Royal Statistical Society, Ser. B, 25, 318-329