Testing relevant hypotheses in functional time series via self-normalization
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Date
2018
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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.
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Keywords
self normalization, relevant hypotheses, CUSUM, change point analysis, two sample problems, functional time series