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NONPARAMETRIC ESTIMATION AND TESTING OF INTERACTION IN ADDITIVE MODELS

Published online by Cambridge University Press:  16 May 2002

Stefan Sperlich ,
Dag Tjøstheim  and
Lijian Yang
Stefan Sperlich
Affiliation:
Universidad Carlos III de Madrid
Dag Tjøstheim
Affiliation:
University of Bergen
Lijian Yang
Affiliation:
Michigan State University
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Abstract

We consider an additive model with second-order interaction terms. Both marginal integration estimators and a combined backfitting-integration estimator are proposed for all components of the model and their derivatives. The corresponding asymptotic distributions are derived. Moreover, two test statistics for testing the presence of interactions are proposed. Asymptotics for the test functions and local power results are obtained. Because direct implementation of the test procedure based on the asymptotics would produce inaccurate results unless the number of observations is very large, a bootstrap procedure is provided, which is applicable for small or moderate sample sizes. Further, based on these methods a general test for additivity is developed. Estimation and testing methods are shown to work well in simulation studies. Finally, our methods are illustrated on a five-dimensional production function for a set of Wisconsin farm data. In particular, the separability hypothesis for the production function is discussed.

Type
Research Article
Information
Econometric Theory , Volume 18 , Issue 2 , April 2002 , pp. 197 - 251
Copyright
© 2002 Cambridge University Press

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