EconStor >
Technische Universität Dortmund >
Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen, Technische Universität Dortmund >
Technical Reports, SFB 475, TU Dortmund >

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10419/49358
  
Title:A simple nonparametric estimator of a monotone regression function PDF Logo
Authors:Dette, Holger
Neumeyer, Natalie
Pilz, Kay F.
Issue Date:2003
Series/Report no.:Technical Report // Universität Dortmund, SFB 475 Komplexitätsreduktion in Multivariaten Datenstrukturen 2003,26
Abstract:In this paper a new method for monotone estimation of a regression function is proposed. The estimator is obtained by the combination of a density and a regression estimate and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series estimators or smoothing splines. The main idea of the new approach is to construct a density estimate from the estimated values ˆm(i/N) (i = 1, . . . ,N) of the regression function to use these “data” for the calculation of an estimate of the inverse of the regression function. The final estimate is then obtained by a numerical inversion. Compared to the conventially used techniques for monotone estimation the new method is computationally more efficient, because it does not require constrained optimization techniques for the calculation of the estimate. We prove asymptotic normality of the new estimate and compare the asymptotic properties with the unconstrained estimate. In particular it is shown that for kernel estimates or local polynomials the monotone estimate is first order asymptotically equivalent to the unconstrained estimate. We also illustrate the performance of the new procedure by means of a simulation study.
Subjects:isotonic regression
order restricted inference
Nadaraya-Watson estimator
local linear regression
Document Type:Working Paper
Appears in Collections:Technical Reports, SFB 475, TU Dortmund

Files in This Item:
File Description SizeFormat
373262450.psOriginal Publication623.11 kBPostscript
373262450.pdf253.41 kBAdobe PDF
No. of Downloads: Counter Stats
Download bibliographical data as: BibTeX
Share on:http://hdl.handle.net/10419/49358

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.