ANCOVA methods for heteroscedastic nonparametric regression models

We consider an ANCOVA design in which the relationship between the response Y-i and the covariate Xi in cell (factor-level combination) i satisfies th e model Y-i = m(i)(X-i) + sigma (i)(X-i)epsilon (i), where the error term e psilon (i) is assumed to be independent of X-i, and m(i) and sigma (i) are respectively a smooth (but unknown) regression and scale function. This mod el can be viewed as a generalization of the nonparametric ANCOVA model of Y oung and Bowman. As such it is a useful alternative for parametric or semip arametric ANCOVA models, whenever modeling assumptions such as proportional odds, normality of the error terms, linearity or homoscedasticity appear s uspect. We develop test statistics for the hypotheses of no main effects, n o interaction effects, and no simple effects, which adjust for the covariat e values, as destined by Akritas,Arnold, and Du. The asymptotic distributio n of the test statistics is obtained, its small sample behavior is studied by means of simulations and a real dataset is analyzed.