Summary: OPTIMAL TESTING FOR ADDITIVITY IN
MULTIPLE NONPARAMETRIC REGRESSION
Short title: Testing Additivity
Department of Statistics and Operations Research,
Tel Aviv University, Tel Aviv 69978, Israel.
Italia De Feis
Istituto per le Applicazioni del Calcolo "Mauro Picone" Sezione di Napoli,
Consiglio Nazionale delle Ricerche, Via Pietro Castellino 111,
80131 Napoli, Italy.
Department of Mathematics and Statistics,
University of Cyprus, P.O. Box 20537, CY 1678 Nicosia, Cyprus.
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 L2([0, 1]d)-norm and also possesses some
smoothness properties. In order to shed some light on the theoretical results obtained,