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NN goodness-of-fit tests for linear models. (English) Zbl 0847.62036
Summary: Let \((X,Y)\) be a random vector in the plane. Consider the decomposition \(Y = m(X) + \varepsilon\), where \(m(x) = \mathbb{E}[Y \mid X = x]\) is the regression of \(Y\) on \(X\). We propose a test for \(H_0:m\) is linear, which is consistent for any nonlinear \(m\). It is based on a comparison of a (fully nonparametric) nearest neigbor and a parametric estimator of \(m\).

MSC:
62G10 Nonparametric hypothesis testing
62G07 Density estimation
62J05 Linear regression; mixed models
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