Ghosh, J. K.; Mukerjee, Rahul Characterization of priors under which Bayesian and frequentist Bartlett corrections are equivalent in the multiparameter case. (English) Zbl 0728.62020 J. Multivariate Anal. 38, No. 2, 385-393 (1991). Summary: In a multiparameter situation, this paper characterizes priors under which the Bayesian and frequentist Bartlett corrections for the likelihood ratio statistic differ by o(1). The role of Jeffreys’ prior in this regard has also been investigated. Cited in 1 ReviewCited in 14 Documents MSC: 62E17 Approximations to statistical distributions (nonasymptotic) 62E20 Asymptotic distribution theory in statistics 62A01 Foundations and philosophical topics in statistics Keywords:characterization of priors; noninformative prior; multiparameter case; frequentist Bartlett corrections; likelihood ratio statistic; Jeffreys’ prior PDFBibTeX XMLCite \textit{J. K. Ghosh} and \textit{R. Mukerjee}, J. Multivariate Anal. 38, No. 2, 385--393 (1991; Zbl 0728.62020) Full Text: DOI References: [1] Barndorff-Nielsen, O. E.; Blaesild, P., A note on the calculation of Bartlett adjustments, J. Roy. Statist. Soc. Ser. B, 48, 353-358 (1986) · Zbl 0623.62045 [2] Barndorff-Nielsen, O. E.; Hall, P., On the level error after Bartlett adjustment of the likelihood ratio statistic, Biometrika, 75, 374-378 (1988) · Zbl 0638.62019 [3] Bickel, P. J.; Ghosh, J. K., A decomposition for the likelihood ratio statistic and the Bartlett correction—A Bayesian argument, Ann. Statist., 18, 1070-1090 (1990) · Zbl 0727.62035 [4] Blight, B. J.N; Rao, P. V., The convergence of Bhattacharya bounds, Biometrika, 61, 137-142 (1974) · Zbl 0285.62011 [5] Chandra, T. K.; Ghosh, J. K., Valid asymptotic expansions for the likelihood ratio statistic and other perturbed chi-square variables, Sankhyā Ser. A, 41, 22-47 (1979) · Zbl 0472.62028 [6] Cox, D. R.; Reid, N., Parameter orthogonality and approximate conditional inference (with discussion), J. Roy. Statist. Soc. Ser. B, 49, 1-39 (1987) · Zbl 0616.62006 [7] Dawid, A. P., Invariant prior distributions, (Kotz, S.; Johnson, N. L., Encyclopedia of Statistical Sciences, Vol. 4 (1983), Wiley: Wiley New York), 228-236 [8] Ghosh, J. K.; Sathe, Y. S., Convergence of Bhattacharya bounds-revisited, Sankhyā Ser. A, 49, 37-42 (1987) · Zbl 0642.62015 [9] Ghosh, J. K.; Sinha, B. K.; Joshi, S. N., Expansions for posterior probability and integrated Bayes risk, (Gupta, S. S.; Berger, J. O., Statistical Decision Theory and Related Topics III, Vol. 1 (1982), Academic Press: Academic Press New York), 403-456 · Zbl 0585.62062 [10] Johnson, R. A., Asymptotic expansions associated with posterior distributions, Ann. Math. Statist., 41, 851-864 (1970) · Zbl 0204.53002 [11] Morris, C. N., Natural exponential families with quadratic variance functions, Ann. Statist., 10, 65-80 (1982) · Zbl 0498.62015 [12] Seth, G. R., On the variance of estimates, Ann. Math. Statist., 20, 1-27 (1949) · Zbl 0032.42003 [13] Shanbhag, D. N., Some characterizations based on the Bhattacharya matrix, J. Appl. Probab., 9, 580-587 (1972) · Zbl 0252.60008 [14] Stein, C., On coverage probability of confidence sets based on a prior distribution, (Sequential Methods in Statistics, Banach Center Publication, Vol. 16 (1985), PWN: PWN Warsaw), 485-514 [15] Welch, B. N.; Peers, H. W., On formulae for confidence points based on integrals of weighted likelihoods, J. Roy. Statist. Soc. B, 25, 318-329 (1963) · Zbl 0117.14205 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.