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Zusammenfassung:
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The main goal of this dissertation is twofold. In the first part, two novel two-
sample tests for matrix data are presented. The theoretical properties of these novel tests are
investigated in the context of testing orthogonal invariance in distribution, while the empirical
values are presented in other cases. The tests are not distribution-free under H0. Therefore,
their quality is investigated through a power study by implementing the warp-speed bootstrap
algorithm. The novel tests are applied to multiple cases of real data, primarily originating in the
field of finance. These tests are the first of their kind for two-sample tests of positive definite
symmetric matrix distributions and are based on Laplace and Hankel transforms.
The second part of this dissertation addresses problems related to data segmentation (or
change point detection). Two novel classes of univariate tests for offline data segmentation
are outlined, and their theoretical properties are studied. The powers are estimated using the
permutation bootstrap algorithm, and the novel tests are shown to have higher test powers than
the well-known tests based on the characteristic function. The location of the change point
is estimated, and the novel tests are empirically demonstrated to possess greater precision.
These tests are applied to two distinct datasets from meteorology and macroeconomics, further
emphasizing their applicability in real-case scenarios.
Moreover, the two-sample test based on the Hankel transform is modified to address change
point problems. The asymptotic properties of this novel test are derived. A power study is
presented, demonstrating the quality of the novel test in small-sample scenarios. The novel
test is applied to financial data, emphasizing the practical applicability of this approach. This
represents the first test for change point inference based on integral transforms for matrix
data. |