Classical Statistical Inference

Abstract

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.