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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
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