Recursive estimation of nonparametric regression with functional covariate

2012/01/01 by Aboubacar Amiri, Amiri, Aboubacar, Christophe Crambes +3
Computer Science · Engineering · Mathematics · #62G05 #62G07 #62G08 #Advanced Statistical Methods and Models #Control Systems and Identification #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1211.2780

openalex publication_date 2012/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main purpose is to estimate the regression function of a real random variable with functional explanatory variable by using a recursive nonparametric kernel approach. The mean square error and the almost sure convergence of a family of recursive kernel estimates of the regression function are derived. These results are established with rates and precise evaluation of the constant terms. Also, a central limit theorem for this class of estimators is established. The method is evaluated on simulations and real data set studies.

Related

• Consistency of the recursive nonparametric regression estimation for dependent functional data
• Advances on nonparametric regression for functional variables
• Nonparametric Estimation of Variance Function for Functional Data
• Asymptotic normality of recursive estimators under strong mixing conditions
• Nonparametric regression for locally stationary functional time series