Some pitfalls of tests of separate families of hypotheses: Normality vs. lognormality

Published

Journal Article

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. © 1991, Taylor & Francis Group, LLC. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Al-Khalidi, HR; Hwang, LJ

Published Date

  • January 1, 1991

Published In

Volume / Issue

  • 20 / 8

Start / End Page

  • 2505 - 2528

Electronic International Standard Serial Number (EISSN)

  • 1532-415X

International Standard Serial Number (ISSN)

  • 0361-0926

Digital Object Identifier (DOI)

  • 10.1080/03610929108830647

Citation Source

  • Scopus