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Key Ideas in Parameter Estimation

Authors:
Pavel Loskot

Keywords: Inference; linear estimator; noise; optimum estimator; parameter estimation; risk function; uncertainty

Abstract:
Parameter estimation plays a crucial role in many applications of statistical signal processing. Estimation theory is a well-established and rigorous framework for making the statistical inferences from noisy observations. It yields the best possible (in a precisely defined sense), interpretable and numerically effective procedures, provided that the models of measurements and of signals are known up to unknown parameters. Understanding the fundamental principles of parameter estimation is nowadays also important in designing the interpretable machine learning architectures, which usually exchange the computational complexity for the superior performance, while alleviating the need for knowing the models of signals and measurements. This paper comprehensively outlines the key principles of estimating the time-invariant random and non-random parameters, which are accompanied by several illustrative examples. The presentation focuses on the key ideas, and does not cover many other relevant topics; for example, neither the estimation of time-varying signals nor the survey of the research literature are considered.

Pages: 18 to 27

Copyright: Copyright (c) IARIA, 2024

Publication date: March 10, 2024

Published in: conference

ISSN: 2519-8432

ISBN: 978-1-68558-142-8

Location: Athens, Greece

Dates: from March 10, 2024 to March 14, 2024