Testing for the Covariate Effect in the Fully Nonparametric ANCOVA

• Activity Number: 305
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Shu-Min Liao*+ and Michael G. Akritas
• Companies: Amherst College and The Pennsylvania State University
• Keywords: Nonparametric ; Analysis of Covariance ; Nested Designs ; Asymptotic Theory

Abstract

In this talk, we introduce a new approach for testing the covariate effect in the context of the fully nonparametric ANCOVA which capitalizes on the connection to the testing problems in two-fold nested designs. The basic idea behind the proposed method is to think of each distinct covariate value as a level of a sub-class nested in each group/class. A projection-based tool is developed to obtain a new class of quadratic forms, whose asymptotic behavior is then studied to establish the limiting distributions of the proposed test statistic under the null hypothesis and local alternatives. Simulation studies show that this new method, compared with existing alternatives, has better power properties and achieves the nominal level under violations of the classical assumptions. Analysis of several data sets are also included.