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Seminario
"Bias and Variance Asymptotic expansions of Maximum likelihood Estimators(MLE): theoretical developments and applications."

Relatore: Michele Zanolin- MIT - Boston

Aula Einstein - Dipartimento di Fisica
02 Ottobre 2003 ore 16.30

Abstract
Bias and Variance Asymptotic expansions of Maximum likelihood Estimators(MLE): theoretical developments and applications. Parameter estimations from measurements of Gaussian observables that are non linearly related with the parameters,or in general from non Gaussian observables, typically presents prohibitive difficulties in quantifyingthe estimate's error. Furthermore, even if the estimate is unbiased, the variance often exceeds the theoretical minimum (Cramer-Rao lower bound)by orders of magnitude. The problem is discussed here by means of asymptotic expansions of MLE's bias and variances in inverse powers of the number of statistically independent samples of the observable.It is also discussed how these expansions, for Gaussian data, can be re-expressed in terms of inverse powers of the signal to noise ratio. Applications to Ocean waveguides, to parameter estimation from gravitational waves, and if there is enough time, to the search for an ocean on a moon of Jupiter will be discussed.