Variable bandwidth kernel regression estimation

2021/01/12 by Janet Nakarmi, Nakarmi, Janet, Hailin Sang +3
Engineering · Mathematics · Medicine · #62E20 #62G07 #62H12 #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Liver Disease Diagnosis and Treatment #Methodology (stat.ME) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2101.04783

openalex publication_date 2021/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we propose a variable bandwidth kernel regression estimator for i.i.d. observations in ℝ² to improve the classical Nadaraya-Watson estimator. The bias is improved to the order of O(h_n⁴) under the condition that the fifth order derivative of the density function and the sixth order derivative of the regression function are bounded and continuous. We also establish the central limit theorems for the proposed ideal and true variable kernel regression estimators. The simulation study confirms our results and demonstrates the advantage of the variable bandwidth kernel method over the classical kernel method.

Related

• Central limit theorem for the variable bandwidth kernel density estimators
• An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions
• Unified treatment of the asymptotics of asymmetric kernel density estimators
• Axiomatic Approach to Variable Kernel Density Estimation
• Uniform in bandwidth consistency of local polynomial regression function estimators