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An adaptive, rate-optimal test of linearity for median regression models. (English) Zbl 1048.62050
Summary: This article is concerned with testing the hypothesis that a conditional median function is linear against a nonparametric alternative with unknown smoothness. We develop a test that is uniformly consistent against alternatives whose distance from the linear model converges to zero at the fastest possible rate. The test does not require knowledge of the distribution of the model’s random noise component, and it permits conditional heteroscedasticity of unknown form. The numerical performance and usefulness of the test are illustrated by the results of Monte Carlo experiments and an empirical example.

MSC:
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62G08 Nonparametric regression and quantile regression
65C05 Monte Carlo methods
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