Arbeitspapier
A simple nonparametric estimator of a monotone regression function
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.
- Sprache
-
Englisch
- Erschienen in
-
Series: Technical Report ; No. 2003,26
- Thema
-
isotonic regression
order restricted inference
Nadaraya-Watson estimator
local linear regression
Regression
Nichtparametrisches Verfahren
Schätztheorie
- Ereignis
-
Geistige Schöpfung
- (wer)
-
Dette, Holger
Neumeyer, Natalie
Pilz, Kay F.
- Ereignis
-
Veröffentlichung
- (wer)
-
Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen
- (wo)
-
Dortmund
- (wann)
-
2003
- Handle
- Letzte Aktualisierung
-
10.03.2025, 11:43 MEZ
Datenpartner
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. Bei Fragen zum Objekt wenden Sie sich bitte an den Datenpartner.
Objekttyp
- Arbeitspapier
Beteiligte
- Dette, Holger
- Neumeyer, Natalie
- Pilz, Kay F.
- Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen
Entstanden
- 2003
Ähnliche Objekte (12)
Strictly monotone and smooth nonparametric regression for two or more variables
On the estimation of a monotone conditional variance in nonparametric regression
A comparative study of monotone nonparametric kernel estimates
Testing strict monotonicity in nonparametric regression
Estimating a convex function in nonparametric regression
A power comparison between nonparametric regression tests
Nonparametric comparison of regression curves - an empirical process approach
Testing for symmetric error distribution in nonparametric regression models
A note on estimating a monotone regression by combining kernel and density estimates
Some methodological aspects of validation of models in nonparametric regression
Testing for a constant coefficient of variation in nonparametric regression
Testing symmetry in nonparametric regression models
Strictly monotone and smooth nonparametric regression for two or more variables
On the estimation of a monotone conditional variance in nonparametric regression
A comparative study of monotone nonparametric kernel estimates
Testing strict monotonicity in nonparametric regression
Estimating a convex function in nonparametric regression
A power comparison between nonparametric regression tests
Nonparametric comparison of regression curves - an empirical process approach
Testing for symmetric error distribution in nonparametric regression models
A note on estimating a monotone regression by combining kernel and density estimates
Some methodological aspects of validation of models in nonparametric regression
Testing for a constant coefficient of variation in nonparametric regression
Testing symmetry in nonparametric regression models
Strictly monotone and smooth nonparametric regression for two or more variables
On the estimation of a monotone conditional variance in nonparametric regression
A comparative study of monotone nonparametric kernel estimates
Testing strict monotonicity in nonparametric regression
Estimating a convex function in nonparametric regression
A power comparison between nonparametric regression tests
Nonparametric comparison of regression curves - an empirical process approach
Testing for symmetric error distribution in nonparametric regression models
A note on estimating a monotone regression by combining kernel and density estimates
Some methodological aspects of validation of models in nonparametric regression
Testing for a constant coefficient of variation in nonparametric regression