A Bartlett-type adjustment for the likelihood ratio statistic with an ordered alternative. (English) Zbl 0801.62015
Summary: For testing the equality of normal variances with an increasing alternative, under the null hypothesis the likelihood ratio test statistic is asymptotically distributed as a mixture of chi-squared distributions. In this paper a Bartlett-type adjustment is proposed to improve the approximation of the null distribution of the likelihood ratio test statistic with an ordered alternative.
MSC:
| 62E17 | Approximations to statistical distributions (nonasymptotic) |
| 62F03 | Parametric hypothesis testing |
| 62E20 | Asymptotic distribution theory in statistics |
| 62F30 | Parametric inference under constraints |
Keywords:
testing the equality of normal variances; increasing alternative; likelihood ratio test; mixture of chi-squared distributions; Bartlett- type adjustment; approximation of the null distribution; ordered alternativeReferences:
| [1] | Abramowitz, M.; Stegun, I. S., Handbook of Mathematical Functions (1965), Dover: Dover New York |
| [2] | Barndorff-Nielsen, O. E.; Cox, D. R., Edgeworth and saddlepoint approximations with statistical applications, J. Roy. Statist. Soc. Ser. 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. Ser. 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, 268-282 (1937) · Zbl 0016.41201 |
| [6] | Bartlett, M. S., A note on the multiplying factors for various \(χ^2\) approximations, J. Roy. Statist. Soc. Ser. B, 16, 296-298 (1954) · Zbl 0057.35404 |
| [7] | 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 |
| [8] | Boswell, M. T.; Brunk, H. D., Distribution of likelihood ratio in testing against trend, Ann. Math. Statist., 40, 371-380 (1969) · Zbl 0255.62022 |
| [9] | Box, G. E.P., A general distribution theory for a class of likelihood criteria, Biometrika, 36, 317-346 (1949) · Zbl 0035.09101 |
| [10] | Brunk, D., On a Theorem of E. Sparre Andersen and its application to tests against trend, Math. Scand., 8, 305-326 (1960) · Zbl 0097.13402 |
| [11] | Hayakawa, T., The likelihood ratio criterion and the asypmtotic expansion of its distribution, Ann. Inst. Statist. Math., 29, 359-378 (1977) · Zbl 0438.62015 |
| [12] | Lawley, D. N., A general method for approximating to the distribution of the likelihood ratio criteria, Biometrika, 43, 295-303 (1956) · Zbl 0073.13602 |
| [13] | Robertson, T.; Wright, F. T.; Dykstra, R. L., Order Restricted Statistical Inferences (1988), Wiley: Wiley New York · Zbl 0645.62028 |
| [14] | Wang, Y., Asymptotic expansions of the likelihood ratio test statistic with ordered hypotheses, Sankhyā Ser A. (1993) |
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.
