Abstract
The main focus of this chapter is the asymptotic Normality and optimality of the maximum likelihood estimator (MLE), under regularity conditions. The Cramér–Rao lower bound for the variance of unbiased estimators of parametric functions is shown to be achieved asymptotically by the MLE. Also derived are the asymptotic Normality of M-estimators and the asymptotic behavior of the Bayes posterior.
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Notes
- 1.
See Lehmann and Casella (1998, p. 448).
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Bhattacharya, R., Lin, L., Patrangenaru, V. (2016). Large Sample Theory of Estimation in Parametric Models. In: A Course in Mathematical Statistics and Large Sample Theory. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-4032-5_7
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DOI: https://doi.org/10.1007/978-1-4939-4032-5_7
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