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Bartlett-type modification for Rao’s efficient score statistic. (English) Zbl 0712.62013

Summary: This paper suggests simple Bartlett-type modifications for a wide class of test statistics that include in particular the efficient score and the likelihood ratio statistics.

MSC:

62E17 Approximations to statistical distributions (nonasymptotic)
Full Text: DOI

References:

[1] Barndorff-Nielsen, O. E., Inference on full or partial parameters based on the standardized signed log likelihood ratio, Biometrika, 73, 307-322 (1986) · Zbl 0605.62020
[2] Barndorff-Nielsen, O. E.; Cox, D. R., Edgeworth and saddle-point approximations with statistical applications (with discussion), J. Roy. Statist. Soc. B, 41, 279-312 (1979) · Zbl 0424.62010
[3] Barndorff-Nielsen, O. E.; Cox, D. R., Bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator, J. Roy. Statist. Soc. B, 46, 483-495 (1984) · Zbl 0581.62016
[4] 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
[5] Bartlett, M. S., Properties of sufficiency and statistical tests, (Proc. Roy. Soc. A, 160 (1937)), 268-282 · Zbl 0016.41201
[6] Bartlett, M. S., A note on the multiplying factors for various \(χ^2\) approximations, J. Roy. Statist. Soc. B, 16, 296-298 (1954) · Zbl 0057.35404
[7] Bhattacharya, R. N., Some recent results on Cramer-Edgeworth expansions with applications, (Krishnaiah, P. R., Multivariate Analysis VI (1985), North-Holland: North-Holland Amsterdam) · Zbl 0588.62029
[8] Bhattacharya, R. N.; Ghosh, J. K., On the validity of the formal Edgeworth expansions, Ann. Statist., 6, 434-451 (1978), Correction, ibid. 8 1399 · Zbl 0396.62010
[9] Bickel, P. J.; Ghosh, J. K., A decomposition for the likelihood ratio statistic and the Bartlett correction—A Bayesian argument, Ann. Statist. (1990), to appear · Zbl 0727.62035
[10] Chandra, T. K., Asymptotic expansions of perturbed chi-square variables, Sankhy \(a\) A, 47, 100-110 (1985) · Zbl 0595.62010
[11] Chandra, T. K.; Ghosh, J. K., Valid asymptotic expansions for the likelihood ratio statistic and other perturbed chi-square variables, Sankhy \(a\) A, 41, 22-47 (1979) · Zbl 0472.62028
[12] Chandra, T. K.; Joshi, S. N., Comparison of the likelihood ratio, Rao’s and Wald’s tests and a conjecture of C. R. Rao, Sankhy \(a\) A, 45, 226-246 (1983) · Zbl 0563.62018
[13] Chandra, T. K.; Mukerjee, R., On the optimality of Rao’s statistic, Commun. Statist.—Theor. Meth., 13, 1507-1515 (1984)
[14] Chandra, T. K.; Samanta, T., On the second-order local comparison between perturbed maximum likelihood estimators and Rao’s statistic as test statistics, J. Multivariate Anal., 25, 201-222 (1988) · Zbl 0655.62018
[15] Cordeiro, G. M.; Paula, G. A., Improved likelihood ratio statistics for exponential famity nonlinear models, Biometrika, 76, 93-100 (1989) · Zbl 0663.62068
[16] Cox, D. R., Some aspects of conditional and asymptotic inference: A review, Sankhy \(a\) A, 50, 314-337 (1988) · Zbl 0676.62031
[17] Cox, D. R.; Reid, N., Parameter orthogonality and approximate conditional inference (with discussion), J. Roy. Statist. Soc. B, 49, 1-39 (1987) · Zbl 0616.62006
[18] Lawley, D. N., A general method for approximating to the distribution of the likelihood ratio criteria, Biometrika, 43, 295-303 (1956) · Zbl 0073.13602
[19] McCullagh, P., Local sufficiency, Biometrika, 71, 233-244 (1984) · Zbl 0573.62026
[20] McCullagh, P., (Tensor Methods in Statistics (1987), Chapman & Hall: Chapman & Hall London) · Zbl 0732.62003
[21] McCullagh, P.; Cox, D. R., Invariants and likelihood ratio statistics, Ann. Statist., 14, 1419-1430 (1986) · Zbl 0615.62041
[22] Mukerjee, R., Third-order comparison of unbiased tests: A simple formula for the power difference in the one-parameter case, Sankhy \(a\) A, 51, 212-232 (1989) · Zbl 0727.62029
[23] Mukerjee, R., Comparison of tests in the presence of a nuisance parameter, (Dodge, Y., Statistical Data Analysis and Inference (1989), North-Holland: North-Holland Amsterdam), 131-139 · Zbl 0735.62027
[24] Mukerjee, R., Comparison of tests in the multiparameter case II. A third-order optimality propety of Rao’s test, J. Multivariate Anal., 33, 31-48 (1990) · Zbl 0703.62029
[25] Rao, C. R., (Linear Statistical Inference and Its Applications (1973), Wiley: Wiley New York) · Zbl 0256.62002
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