Estimating a convex function in nonparametric regression

Holger Dette and Melanie Birke

No 2005,21, Technical Reports from Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen

Abstract: A new nonparametric estimate of a convex regression function is proposed and its stochastic properties are studied. The method starts with an unconstrained estimate of the derivative of the regression function, which is firstly isotonized and then integrated. We prove asymptotic normality of the new estimate and show that it is first order asymptotically equivalent to the initial unconstrained estimate if the regression function is in fact convex. If convexity is not present the method estimates a convex function whose derivative has the same Lp-norm as the derivative of the (non-convex) underlying regression function. The finite sample properties of the new estimate are investigated by means of a simulation study and the application of the new method is demonstrated in two data examples.

Keywords: nonparametric regression; order restricted inference; convexity; Nadaraya-Watson estimate; nondecreasing rearrangement (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:zbw:sfb475:200521

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