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Biometrika 1984 71(3):487-493; doi:10.1093/biomet/71.3.487
© 1984 by Biometrika Trust
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Effective degrees of freedom and the likelihood ratio test

D. R. COX

Department of Mathematics, Imperial College London, U.K.

Normal-theory problems involving several unknown variances may require use of estimates not having simple chi-squared distributions. Confidence intervals are then commonly based on the use of ‘effective degrees of freedom’, i.e. the fitting of a gamma distribution via the first two moments, replacing parameters by estimates. The confidence intervals given by this method are compared with those resulting from the likelihood ratio test, inserting a Bartlett adjustment factor to achieve close approximation by a chi-squared distribution. Two special problems, one concerning components of variance and one a generalization of the Behrens-Fisher problem, are studied in detail.

Key Words: Asymptotic theory • Bartlett factor • Behrens-Fisher problem • Components of variance • Exponential family • Likelihood ratio test


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D R Cox
Components of variance: a miscellany
Statistical Methods in Medical Research, February 1, 1998; 7(1): 3 - 12.
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