TEST FOR COVARIATE EFFECT IN FULLY NONPARAMETRIC ANCOVA MODEL

Lan Wang (joint work with Michael G. Akritas)
Department of Statistics, the Pennsylvania State University, State College, 
PA 16802

At first, we consider testing for no main row in the two-way ANOVA model 
with the levels of the row factor going to infinity. This is an extension 
of the work of Akritas and Papadatos (2001) on heteroscedastic one-way 
ANOVA when treatment levels are large. The projection method is applied
to a suitable quadratic form to obtain the asymptotic distribution of the 
F-statistic. Both homoscedastic and heterosedastic models will be discussed.

We then extend the methodology and ideas above to the fully nonparametric 
ANCOVA model proposed by Akritas, Arnold and Du (2000). This model allows 
the covariate to influence the response in a possibly nonlinear and 
nonpolynomial way. The distributions for each factor level combination 
and covariate values are not restricted to comply with any parametric 
or semiparametric model. Here, I will talk about some results on testing 
for no nonparametric covariate effect.