Abstract
In the Gaussian regression model, we propose a new test, based on model selection methods, for testing that the regression function F belongs to a linear space. The test is free from any prior assumption on F and on the variance a2 of the errors. The procedure is rate optimal over both smooth and directional alternatives and the simulations studies show that it is also robust with respect to the non-Gaussianity of the errors.
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© 2002 Springer Science+Business Media New York
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Baraud, Y., Huet, S., Laurent, B. (2002). A New Test of Linear Hypothesis in Regression. In: Huber-Carol, C., Balakrishnan, N., Nikulin, M.S., Mesbah, M. (eds) Goodness-of-Fit Tests and Model Validity. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0103-8_15
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DOI: https://doi.org/10.1007/978-1-4612-0103-8_15
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6613-6
Online ISBN: 978-1-4612-0103-8
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