A Nonparametric Bootstrap Method for Heteroscedastic Functional Data

Abstract

The objective is to provide a nonparametric bootstrap method for functional data that consists of independent realizations of a continuous one-dimensional process. The process is assumed to be nonstationary, with a functional mean and a functional variance, and dependent. The resampling method is based on nonparametric estimates of the model components. Numerical studies were conducted to check the performance of the proposed procedure, by approximating the bias and the standard error of two estimators. A practical application of the proposed approach to pollution data has also been included. Specifically, it is employed to make inference about the annual trend of ground-level ozone concentration at Yarner Wood monitoring station in the United Kingdom. Supplementary material to this paper is provided online.