Testing additivity by kernel based methods - what is a reasonable test?
Loading...
Date
2000
Journal Title
Journal ISSN
Volume Title
Publisher
Universitätsbibliothek Dortmund
Abstract
In the common nonparametric regression model with high dimensional predictor several tests for the hypothesis of an additive regression are investigated. The corresponding test statistics are either based on the differences between a fit under the assumption of additivity and a fit in the general model or based on residuals under the assumption of additivity. For all tests asymptotic normality is established under the null hypothesis of additivity and under fixed alternatives with different rates of convergence corresponding to both cases. These results are used for a comparison of the different methods. It is demonstrated that a statistic based on an empirical L2 distance of the Nadaraya Watson and the marginal integration estimator yields the (asymptotically) most efficient procedure, if these are compared with respect to the asymptotic behaviour under fixed alternatives.
Description
Table of contents
Keywords
additive models, dimension reduction, test of additivity, marginal integration estimate