Optimal testing for additivity in multiple nonparametric regression
Date
2009Source
Annals of the Institute of Statistical MathematicsVolume
61Issue
3Pages
691-714Google Scholar check
Keyword(s):
Metadata
Show full item recordAbstract
We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) non- adaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L 2([0, 1] d )-norm and also possesses some smoothness properties. In order to shed some light on the theoretical results obtained, we carry out a wide simulation study to examine the finite sample performance of the proposed hypothesis testing procedures and compare them with a series of other tests for additivity available in the literature. © 2008 The Institute of Statistical Mathematics, Tokyo.