On stochastic orderings of the Wilcoxon Rank Sum test statistic--With applications to reproducibility probability estimation testing
Recently, the possibility of testing statistical hypotheses through the estimate of the reproducibility probability (i.e. the estimate of the power of the statistical test) in a general parametric framework has been introduced. In this paper, we provide some results on the stochastic orderings of the Wilcoxon Rank Sum (WRS) statistic, implying, for example, that the related test is strictly unbiased. Moreover, under some regularity conditions, we show that it is possible to define a continuous and strictly monotone power function of the WRS test. This last result is useful in order to obtain a point estimator and lower bounds for the power of the WRS test. In analogy with the parametric setting, we show that these power estimators, alias reproducibility probability estimators, can be used as test statistic, i.e. it is possible to refer directly to the estimate of the reproducibility probability to perform the WRS test. Some reproducibility probability estimators based on asymptotic approximations of the power are provided. A brief simulation shows a very high agreement between the approximated reproducibility probability based tests and the classical one.
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): 81 (2011)
Issue (Month): 8 (August)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- De Martini, Daniele, 2008. "Reproducibility probability estimation for testing statistical hypotheses," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1056-1061, July.
- B. Rosner & R. J. Glynn, 2009. "Power and Sample Size Estimation for the Wilcoxon Rank Sum Test with Application to Comparisons of C Statistics from Alternative Prediction Models," Biometrics, The International Biometric Society, vol. 65(1), pages 188-197, 03.
When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:937-946. 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: (Shamier, Wendy)
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.