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The likelihood ratio criterion and the asymptotic expansion of its distribution. (English) Zbl 0438.62015


MSC:

62E20 Asymptotic distribution theory in statistics
62H15 Hypothesis testing in multivariate analysis
62F03 Parametric hypothesis testing
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References:

[1] Box, G. E. P. (1949). A general distribution theory for a class of likelihood criteria,Biometrika,36, 317–346. · Zbl 0035.09101
[2] Davidson, R. R. and Lever, W. E. (1970). The limiting distribution of the likelihood ratio statistic under a class of local alternatives,Sankhyã,32, 209–224. · Zbl 0217.51003
[3] Fujikoshi, Y. (1970). Asymptotic expansions of the distributions of test statistics in multivariate analysis,Jour. Sci. Hiroshima Univ., Ser. A-I Math.34, 73–144. · Zbl 0208.20602
[4] Hayakawa, T. (1975). The likelihood ratio criterion for a composite hypothesis under a local alternative,Biometrika,62, 451–460. · Zbl 0312.62018 · doi:10.1093/biomet/62.2.451
[5] Lawley, D. N. (1956). A general method for approximating to the distribution of the likelihood ratio criteria,Biometrika,43, 295–303. · Zbl 0073.13602
[6] Lee, J. C., Krishnaiah, P. R. and Chang, T. C. (1976). On the distribution of the likelihood ratio test statistic for compound symmetry,S. Afric. Statist. J.,10, 49–62. · Zbl 0338.62029
[7] Mann, H. B. and Wald, A. (1943). On the stochastic limit and order relationships,Ann. Math. Statist.,14, 217–226. · Zbl 0063.03774 · doi:10.1214/aoms/1177731415
[8] Neyman, J. and Pearson, E. S. (1928). On the use and interpretation of certain test criteria for purposes of statistical inference,Biometrika,20A, 175–240, 263–294. · JFM 54.0565.05
[9] Peers, H. W. (1971). Likelihood ratio and associate test criteria,Biometrika,58, 577–587. · Zbl 0245.62026 · doi:10.1093/biomet/58.3.577
[10] Sugiura, N. and Fujikoshi, Y. (1969). Asymptotic expansions of the non-null distributions of the likelihood ratio criteria for multivariate linear hypothesis and independence.Ann. Math. Statist. 40, 942–952. · Zbl 0184.22303 · doi:10.1214/aoms/1177697599
[11] Sugiura, N. (1969). Asymptotic expansions of the distributions of the likelihood ratio criteria for covariance matrix,Ann. Math. Statist.,40, 2051–2063. · Zbl 0208.44901 · doi:10.1214/aoms/1177697285
[12] Wilks, S. S. (1938). The large sample distribution of the likelihood ratio for testing composite hypothesis,Ann. Math. Statist.,9, 60–62. · Zbl 0018.32003 · doi:10.1214/aoms/1177732360
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