Power transformations to induce normality and their applications
Random variables which are positive linear combinations of positive independent random variables can have heavily right-skewed finite sample distributions even though they might be asymptotically normally distributed. We provide a simple method of determining an appropriate power transformation to improve the normal approximation in small samples. Our method contains the Wilson-Hilferty cube root transformation for "χ"-super-2 random variables as a special case. We also provide some important examples, including test statistics of goodness-of-fit and tail index estimators, where such power transformations can be applied. In particular, we study the small sample behaviour of two goodness-of-fit tests for time series models which have been proposed recently in the literature. Both tests are generalizations of the popular Box-Ljung-Pierce portmanteau test, one in the time domain and the other in the frequency domain. A power transformation with a finite sample mean and variance correction is proposed, which ameliorates the small sample effect. It is found that the corrected versions of the tests have markedly better size properties. The correction is also found to result in an overall increase in power which can be significant under certain alternatives. Furthermore, the corrected tests also have better power than the Box-Ljung-Pierce portmanteau test, unlike the uncorrected versions. Copyright 2004 Royal Statistical Society.
If 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.
Volume (Year): 66 (2004)
Issue (Month): 1 ()
|Contact details of provider:|| Postal: 12 Errol Street, London EC1Y 8LX, United Kingdom|
Web page: http://wileyonlinelibrary.com/journal/rssb
More information through EDIRC
|Order Information:||Web: http://ordering.onlinelibrary.wiley.com/subs.asp?ref=1467-9868&doi=10.1111/(ISSN)1467-9868|
When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:66:y:2004:i:1:p:117-130. See general 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.