Abstract
We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) non- adaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L 2([0, 1]d)-norm and also possesses some smoothness properties. In order to shed some light on the theoretical results obtained, we carry out a wide simulation study to examine the finite sample performance of the proposed hypothesis testing procedures and compare them with a series of other tests for additivity available in the literature.
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Abramovich, F., De Feis, I. & Sapatinas, T. Optimal testing for additivity in multiple nonparametric regression. Ann Inst Stat Math 61, 691–714 (2009). https://doi.org/10.1007/s10463-007-0164-y
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DOI: https://doi.org/10.1007/s10463-007-0164-y