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Model Selection for Signal Processing: a Minimum Error Approach and a General Performance Analysis. (arXiv:2010.11114v1 [eess.SP])

[Submitted on 21 Oct 2020]

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Abstract: Estimation of the number of signals in the presence of noise is an important
problem in several areas of statistical signal processing. There are a lot of
modern works on the design of an optimal solution to this problem in terms of
some criteria. Each criterion generates a model order selection (MOS)

However, the minimum error probability criterion has not received significant
attention, despite the fact that errors in the estimation of the number of
signals might directly affect the performance of the signal processing system
as a whole. In this paper, we propose a new approach to the design of MOS
algorithms partially based on the minimum error probability criterion.

Also, we pay a lot of attention to the performance and consistency analysis
of the MOS algorithms. In this study, an abridged error probability is used as
a universal performance measure of the MOS algorithms. We propose a theoretical
framework that allows to obtain closed-form expressions for the abridged error
probabilities of a wide range of MOS algorithms. Moreover, a parametric
consistency analysis of the presented MOS algorithms is provided.

Next, we use the obtained results to provide a parametric optimization of the
presented MOS algorithms.

Finally, we study a quasilikelihood (QL) approach to the design and analysis
of the MOS algorithms. The proposed theoretical framework is used to obtain the
abridged error probabilities as functions of the unknown signal parameter.
These functions, in its turn, allow us to find the scope of the QL approach.

Submission history

From: Aleksandr Kharin [view email]

Wed, 21 Oct 2020 16:24:35 UTC (633 KB)

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