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Nonparametric estimation and testing of interaction in additive models

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  • Tjostheim, Dag
  • Yang, Lijian

Abstract

We consider an additive model with second order interaction terms. Both marginal integration estimators and backfiting-integration efficient estimators are proposed for all components of the model and their derivatives, together with their explicitly derived asymptotic distributions. Moreover, two test statistics for testing the presence of interactions are proposed. Asymptotics for the test functions and local power results are obtained. Since 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 proposed. 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.

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  • Tjostheim, Dag & Yang, Lijian, 1999. "Nonparametric estimation and testing of interaction in additive models," DES - Working Papers. Statistics and Econometrics. WS 6387, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6387
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    1. Fan, J. & Härdle, Wolfgang & Mammen, Enno, 1996. "Direct estimation of low dimensional components in additive models," SFB 373 Discussion Papers 1996,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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