Resource title

Estimating a convex function in nonparametric regression

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Resource description

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.

Resource author

Holger Dette, Melanie Birke

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Resource publish date

Resource language

eng

Resource content type

text/html

Resource resource URL

http://hdl.handle.net/10419/22612

Resource license

Adapt according to the presented license agreement and reference the original author.