Arbeitspapier

Strictly monotone and smooth nonparametric regression for two or more variables

to connected objects

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.

Language: Englisch

Bibliographic citation: Series: Technical Report ; No. 2005,17

Subject: multivariate nonparametric regression
isotonic regression
order restricted inference
nondecreasing rearrangement
Regression
Nichtparametrisches Verfahren
Theorie

Event: Geistige Schöpfung

(who): Scheder, Regine
Dette, Holger

Event: Veröffentlichung

(who): Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen

(where): Dortmund

(when): 2005

Handle: http://hdl.handle.net/10419/22608

Last update: 10.03.2025, 11:41 AM CET

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Object type

Arbeitspapier

Associated

Scheder, Regine
Dette, Holger
Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen

Time of origin

2005

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