Nonparametric Estimation and Testing of Interaction in Additive Models

Nonparametric Estimation and Testing of Interaction in Additive Models (2002)

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by Stefan Sperlich , Dag Tjstheim , Lijian Yang

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@MISC{Sperlich02nonparametricestimation,
    author = {Stefan Sperlich and Dag Tjstheim and Lijian Yang},
    title = {Nonparametric Estimation and Testing of Interaction in Additive Models},
    year = {2002}
}

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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. 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 developed. Estimation and testing methods are shown to work well in simulation studies. Finally, our methods

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