On Tests for a Normal Mean with Known Coefficient of Variation
AbstractHinkley (1977) derived two tests for testing the mean of a normal distribution with known coefficient of variation (c.v.) for right alternatives. They are the locally most powerful (LMP) and the conditional tests based on the ancillary statistic for μ. In this paper, the likelihood ratio (LR) and Wald tests are derived for the one- and two-sided alternatives, as well as the two-sided version of the LMP test. The performances of these tests are compared with those of the classical "t", sign and Wilcoxon signed rank tests. The latter three tests do not use the information on c.v. Normal approximation is used to approximate the null distribution of the test statistics except for the "t" test. Simulation results indicate that all the tests maintain the type-I error rates, that is, the attained level is close to the nominal level of significance of the tests. The power functions of the tests are estimated through simulation. The power comparison indicates that for one-sided alternatives the LMP test is the best test whereas for the two-sided alternatives the LR or the Wald test is the best test. The "t", sign and Wilcoxon signed rank tests have lower power than the LMP, LR and Wald tests at various alternative values of μ. The power difference is quite large in several simulation configurations. Further, it is observed that the "t", sign and Wilcoxon signed rank tests have considerably lower power even for the alternatives which are far away from the null hypothesis when the c.v. is large. To study the sensitivity of the tests for the violation of the normality assumption, the type I error rates are estimated on the observations of lognormal, gamma and uniform distributions. The newly derived tests maintain the type I error rates for moderate values of c.v. Copyright 2007 The Authors. Journal compilation (c) 2007 International Statistical Institute.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by International Statistical Institute in its journal International Statistical Review.
Volume (Year): 75 (2007)
Issue (Month): 2 (08)
Contact details of provider:
Postal: P.O. Box 950, 2270 AZ Voorburg
Web page: http://www.blackwellpublishing.com/journal.asp?ref=0306-7734
More information through EDIRC
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.