Abstract #300868

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JSM 2003 Abstract #300868
Activity Number: 209
Type: Contributed
Date/Time: Tuesday, August 5, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #300868
Title: Area Based Testing Under Likelihood Ratio Ordering
Author(s): Christopher A. Carolan*+ and Joshua M. Tebbs
Companies: University of Iowa and Oklahoma State University
Address: 2707B Richard Dr., Greenville, NC, 27834-7890,
Keywords: likelihood ratio ordering ; ordinal dominance curve ; least concave majorant ; ROC curve
Abstract:

The ordinal dominance curve formed by the one-sample and two-sample MLE estimators of two cumulative distribution functions F and G under likelihood ratio ordering possesses a very appealing geometric interpretation in terms of the ordinal dominance curve formed by the traditional empirical estimates of F and G. This geometric interpretation, a least concave majorant, suggests some natural testing procedures. The Mann-Whitney test statistic is the area under the ordinal dominance curve formed by the traditional empirical estimates of F and G. Under a likelihood ratio ordering constraint, a natural test statistic would be the area under the restricted or concave ordinal dominance curve. Tests are suggested for testing equality of F and G versus likelihood ratio ordering and likelihood ratio ordering versus all alternatives.

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