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

2017/10/13 by Konstantinos Fokianos, Anne Leucht, Fokianos, Konstantinos +3
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1710.04813

openalex publication_date 2017/10/13 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We consider a general monotone regression estimation where we allow for independent and dependent regressors. We propose a modification of the classical isotonic least squares estimator and establish its rate of convergence for the integrated L₁-loss function. The methodology captures the shape of the data without assuming additivity or a parametric form 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.

Related

• Isotonic regression in general dimensions
• Generalized Asymptotic Limit Theory and Inference for Isotonic Regression
• Least squares estimation in the monotone single index model
• M-estimators for Isotonic Regression
• Technical report: Adaptivity and optimality of the monotone least squares estimator for four different models