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November 2019 Moving block and tapered block bootstrap for functional time series with an application to the $K$-sample mean problem
Dimitrios Pilavakis, Efstathios Paparoditis, Theofanis Sapatinas
Bernoulli 25(4B): 3496-3526 (November 2019). DOI: 10.3150/18-BEJ1099

Abstract

We consider infinite-dimensional Hilbert space-valued random variables that are assumed to be temporal dependent in a broad sense. We prove a central limit theorem for the moving block bootstrap and for the tapered block bootstrap, and show that these block bootstrap procedures also provide consistent estimators of the long run covariance operator. Furthermore, we consider block bootstrap-based procedures for fully functional testing of the equality of mean functions between several independent functional time series. We establish validity of the block bootstrap methods in approximating the distribution of the statistic of interest under the null and show consistency of the block bootstrap-based tests under the alternative. The finite sample behaviour of the procedures is investigated by means of simulations. An application to a real-life dataset is also discussed.

Citation

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Dimitrios Pilavakis. Efstathios Paparoditis. Theofanis Sapatinas. "Moving block and tapered block bootstrap for functional time series with an application to the $K$-sample mean problem." Bernoulli 25 (4B) 3496 - 3526, November 2019. https://doi.org/10.3150/18-BEJ1099

Information

Received: 1 October 2017; Revised: 1 July 2018; Published: November 2019
First available in Project Euclid: 25 September 2019

zbMATH: 07110146
MathSciNet: MR4010963
Digital Object Identifier: 10.3150/18-BEJ1099

Keywords: $K$-sample mean problem , functional time series , mean function , Moving block bootstrap , spectral density operator , tapered block bootstrap

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 4B • November 2019
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