Nonparametric Estimation And Testing Of Interaction In Additive Models
We consider an additive model with second order interaction terms. It is shown how the components of this model can be estimated using marginal integration, and the asymptotic distribution of the estimators is derived. Moreover, two test statistics for testing the presence of interactions are proposed. Asymptotics for the test functions are obtained, but in this case the asymptotics produce inaccurate results unless the number of observations is very large. For small or moderate sample sizes a bootstrap procedure is suggested and is shown to work well on a simulated example. 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.
(This abstract was borrowed from another version of this item.)
Volume (Year): 18 (2002)
Issue (Month): 02 (April)
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- J. FAN & Wolfgang HÄRDLE & Enno MAMMEN, 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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- Wolfgang HÄRDLE & O. LINTON, 1995. "Nonparametric Regression," SFB 373 Discussion Papers 1995,29, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Denny, Michael & Fuss, Melvyn A, 1977. "The Use of Approximation Analysis to Test for Separability and the Existence of Consistent Aggregates," American Economic Review, American Economic Association, vol. 67(3), pages 404-418, June. Full references (including those not matched with items on IDEAS)
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