Component analysis for additive models - Wolfgang Härdle; Stefan Sperlich; Vladimir G. Spokoiny (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 1997)
We consider the component analysis problem for a regression model with an additive structure. The problem is to check the hypothesis of linearity for each component without specifying the structure of the remaining components. In this paper we show that under mild conditions on the design and smoothness of the regression function, each component can be tested with the rate corresponding to the case if all the remaining components were known. The proposed procedure is based on the Haar transform and it is computationally straightforward.
urn:nbn:de:kobv:11-10064328
Keywords: 330; additive model; component analysis; Haar basis; hypothesis of linearity; nonparametric alternative; regression