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.
Publisher Information: Bamberg : Otto-Friedrich-Universität
Year of publication: 2022
Pages: 1-35
Source/Other editions: IEEE Transactions on Information Theory. - 66 (2020) 10
is version of: 10.1109/TIT.2020.3013390
Year of first publication: 2020
Language(s): English
DOI: 10.20378/irb-55002
Licence: German Act on Copyright 
URN: urn:nbn:de:bvb:473-irb-550020
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   
Type: Preprint
URI: https://fis.uni-bamberg.de/handle/uniba/55002
Release Date: 3. February 2023

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