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This book generalizes and extends the available theory in robust
and decentralized hypothesis testing. In particular, it presents a
robust test for modeling errors which is independent from the
assumptions that a sufficiently large number of samples is
available, and that the distance is the KL-divergence. Here, the
distance can be chosen from a much general model, which includes
the KL-divergence as a very special case. This is then extended by
various means. A minimax robust test that is robust against both
outliers as well as modeling errors is presented. Minimax
robustness properties of the given tests are also explicitly proven
for fixed sample size and sequential probability ratio tests. The
theory of robust detection is extended to robust estimation and the
theory of robust distributed detection is extended to classes of
distributions, which are not necessarily stochastically bounded. It
is shown that the quantization functions for the decision rules can
also be chosen as non-monotone. Finally, the book describes the
derivation of theoretical bounds in minimax decentralized
hypothesis testing, which have not yet been known. As a timely
report on the state-of-the-art in robust hypothesis testing, this
book is mainly intended for postgraduates and researchers in the
field of electrical and electronic engineering, statistics and
applied probability. Moreover, it may be of interest for students
and researchers working in the field of classification, pattern
recognition and cognitive radio.
This book generalizes and extends the available theory in robust
and decentralized hypothesis testing. In particular, it presents a
robust test for modeling errors which is independent from the
assumptions that a sufficiently large number of samples is
available, and that the distance is the KL-divergence. Here, the
distance can be chosen from a much general model, which includes
the KL-divergence as a very special case. This is then extended by
various means. A minimax robust test that is robust against both
outliers as well as modeling errors is presented. Minimax
robustness properties of the given tests are also explicitly proven
for fixed sample size and sequential probability ratio tests. The
theory of robust detection is extended to robust estimation and the
theory of robust distributed detection is extended to classes of
distributions, which are not necessarily stochastically bounded. It
is shown that the quantization functions for the decision rules can
also be chosen as non-monotone. Finally, the book describes the
derivation of theoretical bounds in minimax decentralized
hypothesis testing, which have not yet been known. As a timely
report on the state-of-the-art in robust hypothesis testing, this
book is mainly intended for postgraduates and researchers in the
field of electrical and electronic engineering, statistics and
applied probability. Moreover, it may be of interest for students
and researchers working in the field of classification, pattern
recognition and cognitive radio.
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