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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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