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Testing for additivity in non-parametric regression. (English. French summary) Zbl 1357.62197
Summary: This article discusses a novel approach for testing for additivity in non-parametric regression. We represent the model using a linear mixed model framework and equivalently rewrite the original testing problem as testing for a subset of zero variance components. We propose two testing procedures: the restricted likelihood ratio test and the generalized $$F$$ test. We develop the finite sample null distribution of the restricted likelihood ratio test and generalized $$F$$ test using the spectral decomposition of the restricted likelihood ratio and the residual sum of squares, respectively. The null distribution is non-standard and we provide a fast algorithm to simulate from the null distribution of the tests. We show, through numerical investigation, that the proposed testing procedures outperform the available alternatives and apply the methods to a diabetes data set.
##### MSC:
 62G10 Nonparametric hypothesis testing 62G08 Nonparametric regression and quantile regression 62J12 Generalized linear models (logistic models) 62P10 Applications of statistics to biology and medical sciences; meta analysis
##### Software:
ElemStatLearn; gamair; gss; hgam; NNLS; SemiPar
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