Authors: Dette, Holger
Scheder, Regine
Title: Strictly monotone and smooth nonparametric regression for two or more variables
Language (ISO): en
Abstract: In this article a new monotone nonparametric estimate for a regression function of two or more variables is proposed. The method starts with an unconstrained nonparametric regression estimate and uses successively one-dimensional isotonization procedures. In the case of a strictly monotone regression function, it is shown that the new estimate is first order asymptotic equivalent to the unconstrained estimate, and asymptotic normality of an appropriate standardization of the estimate is established. Moreover, if the regression function is not monotone in one of its arguments, the constructed estimate has approximately the same Lp-norm as the initial unconstrained estimate. The methodology is also illustrated by means of a simulation study, and two data examples are analyzed. AMS Subject Classification: 62G05, 62G20
Subject Headings: Isotonic regression
Multivariate nonparametric regression
Nondecreasing rearrangement
Order restricted inference
URI: http://hdl.handle.net/2003/21514
http://dx.doi.org/10.17877/DE290R-6670
Issue Date: 2005-07-07T12:28:29Z
Appears in Collections:Sonderforschungsbereich (SFB) 475

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