Some pitfalls of tests of separate families of hypotheses: normality vs. lognormality |
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Authors: | H R Al-Khalidi L J Hwang |
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Institution: | 1. Department of Epidemiology , University of Texas Health Center at Tyler Tyler , Texas, 75710, U.S.A.;2. Division of Biostatistics , University of Virginia School of Medicine Charlottesville , Virginia, 22908, U.S.A. |
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Abstract: | It is often desirable to test non-nested hypotheses. Cox (1961, 1962) proposed forming a log-likelihood ratio from their maxima and then comparing this value to its expected value under the null hypothesis. Pitfalls exists when we apply Cox's test to the special case of testing normality versus lognormality. Pesaran (1981) and Kotz (1973) pointed out the slow convergence rate of the Cox's test. In this paper, this fact has been reemphasized; moreover, we propose an alternative likelihood ratio test which remedies problems arising from negative estimates of the asymptotic variance of Cox's test statistic and is uniformly more powerful than most commonly used tests. |
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Keywords: | asymptotic variance composite hypothesis convergence log-likelihood ratio maximum likelihood non-nested hypotheses power |
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