A Wild Bootstrap Procedure for the Identification of Optimal Groups in Singular Spectrum Analysis
arxiv(2024)
摘要
A key step in separating signal from noise using Singular Spectrum Analysis
(SSA) is grouping, which is often done subjectively. In this article a method
which enables the identification of statistically significant groups for the
grouping step in SSA is presented. The proposed procedure provides a more
objective and reliable approach for separating noise from the main signal in
SSA. We utilize the w- correlation and test if it close or equal to zero. A
wild bootstrap approach is used to determine the distribution of the
w-correlation. To identify an ideal number of groupings which leads to almost
perfect separation of the noise and signal, a given number of groups are
tested, necessitating accounting for multiplicity. The effectiveness of our
method in identifying the best group is demonstrated through a simulation
study, furthermore, we have applied the approach to real world data in the
context of neuroimaging. This research provides a valuable contribution to the
field of SSA and offers important insights into the statistical properties of
the w-correlation distribution. The results obtained from the simulation
studies and analysis of real-world data demonstrate the effectiveness of the
proposed approach in identifying the best groupings for SSA.
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