The bootstrap in kernel regression for stationary ergodic data when both response and predictor are functions

JOURNAL OF MULTIVARIATE ANALYSIS

卷:173

Article

Krebs, Johannes T. N.¹ 

[1] Univ Calif Davis, Dept Stat, One Shields Ave, Davis, CA 95616 USA

关键词: Confidence sets;    Functional spatial processes;    Functional time series;    Functional kernel regression;    Hilbert spaces;    Naive bootstrap;    Nonparametric regression;    Resampling;    Stationary ergodic data;    Wild bootstrap;   

DOI  :  10.1016/j.jmva.2019.05.004

来源: Elsevier

【 摘 要 】

We consider the double functional regression model Y = r(X) + epsilon, where the response variable Y is Hilbert space-valued and the covariate X takes values in a pseudometric space. The data satisfy an ergodicity criterion which dates back to Laib and Louani (2010) and are arranged in a triangular array. So our model also applies to samples obtained from spatial processes, e.g., stationary random fields. We study a kernel estimator of the Nadaraya-Watson type for the operator r and derive its limiting law which is a Gaussian operator on the Hilbert space. Moreover, we investigate both a naive and a wild bootstrap procedure in the double functional setting and demonstrate their asymptotic validity. This is quite useful as building confidence sets based on an asymptotic Gaussian distribution is often difficult. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free