On likelihood ratio testing for penalized splines

Sonja Greven () and Ciprian Crainiceanu ()

AStA Advances in Statistical Analysis, 2013, vol. 97, issue 4, 387-402

Abstract: Penalized spline regression using a mixed effects representation is one of the most popular nonparametric regression tools to estimate an unknown regression function $$f(\cdot )$$ . In this context testing for polynomial regression against a general alternative is equivalent to testing for a zero variance component. In this paper, we fill the gap between different published null distributions of the corresponding restricted likelihood ratio test under different assumptions. We show that: (1) the asymptotic scenario is determined by the choice of the penalty and not by the choice of the spline basis or number of knots; (2) non-standard asymptotic results correspond to common penalized spline penalties on derivatives of $$f(\cdot )$$ , which ensure good power properties; and (3) standard asymptotic results correspond to penalized spline penalties on $$f(\cdot )$$ itself, which lead to sizeable power losses under smooth alternatives. We provide simple and easy to use guidelines for the restricted likelihood ratio test in this context. Copyright Springer-Verlag Berlin Heidelberg 2013

Keywords: Boundary hypothesis; Likelihood-ratio test; Non-regular problem; Random effect; Restricted maximum likelihood; Variance component (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10182-013-0214-0

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