Authors: Dette, Holger
Kokot, Kevin
Volgushev, Stanislav
Title: Testing relevant hypotheses in functional time series via self-normalization
Language (ISO): en
Abstract: In this paper we develop methodology for testing relevant hypotheses in a tuning-free way. Our main focus is on functional time series, but extensions to other settings are also discussed. Instead of testing for exact equality, for example for the equality of two mean functions from two independent time series, we propose to test a relevant deviation under the null hypothesis. In the two sample problem this means that an L2-distance between the two mean functions is smaller than a pre-specified threshold. For such hypotheses self-normalization, which was introduced by Shao (2010) and Shao and Zhang (2010) and is commonly used to avoid the estimation of nuisance parameters, is not directly applicable. We develop new self-normalized procedures for testing relevant hypotheses in the one sample, two sample and change point problem and investigate their asymptotic properties. Finite sample properties of the proposed tests are illustrated by means of a simulation study and a data example.
Subject Headings: self normalization
relevant hypotheses
CUSUM
change point analysis
two sample problems
functional time series
Subject Headings (RSWK): Hypothesentest
Zeitreihe
URI: http://hdl.handle.net/2003/37138
http://dx.doi.org/10.17877/DE290R-19134
Issue Date: 2018
Appears in Collections:Sonderforschungsbereich (SFB) 823

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