On Integrated L1 Convergence Rate of an Isotonic Regression Estimator for Multivariate Observations

Faculty/Professorship: Mathematics for Business and Economics  
Author(s): Fokianos, Konstantinos; Leucht, Anne  ; Neumann, Michael H.
Title of the Journal: IEEE Transactions on Information Theory
Publisher Information: IEEE
Year of publication: 2020
Volume: 66
Issue: 10
Pages: 6389-6402
Language(s): English
DOI: 10.1109/TIT.2020.3013390
We consider a general monotone regression estimation where we allow for independent and dependent regressors. We propose a modifcation of the classical isotonic least squares estimator and establish its rate of convergence for the integrated L1-loss function. Themethodology captures the shape of the data without assuming additivity or a parametricform for the regression function. Furthermore, the degree of smoothing is chosen automatically and no auxiliary tuning is required for the theoretical analysis. Some simulations and two real data illustrations complement the study of the proposed estimator.
GND Keywords: Isotone Regression; Methode der kleinsten Quadrate; Multivariate Analyse
Keywords: Isotonic least squares estimation, multivariate isotonic regression
DDC Classification: 330 Economics  
RVK Classification: QH 170   
Peer Reviewed: Ja
International Distribution: Ja
Type: Article
URI: https://fis.uni-bamberg.de/handle/uniba/48776
Release Date: 5. October 2020