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Operational Modal Analysis
This chapter introduces the classical statistical approach for system identification in a general context. This is commonly referred as a ‘non-Bayesian’ approach and is currently the conventional perspective in operational modal analysis. Basic quantification of statistical estimators are presented and illustrated with examples. The Cramér-Rao bound and Fisher information matrix are presented to provide the theoretical lower bound for the variance of unbiased estimators. Maximum likelihood estimators and their asymptotic properties for large data size are discussed. The Bayesian and classical statistical approach have different philosophies but share some similarities in mathematics. These shall be discussed so that the two approaches can be applied correctly and advantage can be taken of their mathematical tools developed.
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Cramér H (1946) Mathematical methods of statistics. Princeton University Press, NJ
MATH
Gilbert GT (1991) Positive definite matrices and Sylvester’s criterion. Am Math Monthly 98(1):44–46
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Meyer CD (2000) Matrix analysis and applied linear algebra. Society for Industrial and Applied Mathematics, PA
CrossRef
Rao CR (1945) Information and the accuracy attainable in the estimation of statistical parameters. Bull Calcutta Math Soc 37:81–89
MathSciNetMATH
- Titel
- Classical Statistical Inference
- DOI
- https://doi.org/10.1007/978-981-10-4118-1_9
- Autor:
-
Siu-Kui Au
- Verlag
- Springer Singapore
- Sequenznummer
- 9
- Kapitelnummer
- Chapter 9