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Asymptotic Statistics by A.W. van der Vaart

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8

Efficiency of Estimators

           One purpose of asymptotic statistics is to compare the performance of estimators for large sample sizes. This chapter discusses asymptotic lower bounds for estimation in locally asymptotically normal models. These show, among others, in what sense maximum likelihood estimators are asymptotically efficient.

8.1 Asymptotic Concentration

Suppose the problem is to estimate ψ(θ) based on observations from a model governed by the parameter θ. What is the best asymptotic performance of an estimator sequence Tn for ψ(θ)?

    To simplify the situation, we shall in most of this chapter assume that the sequence image converges ...

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