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Information amount and higher-order efficiency in estimation. (English) Zbl 0703.62031

Summary: By means of second-order asymptotic approximation, the paper clarifies the relationship between the Fisher information of first-order asymptotically efficient estimators and their decision-theoretic performance. It shows that if the estimators are modified so that they have the same asymptotic bias, the information amount can be connected with the risk based on convex loss functions in such a way that the greater information loss of an estimator implies its greater risk. The information loss of the maximum likelihood estimator is shown to be minimal in a general set-up. A multinomial model is used for illustration.

MSC:

62F12 Asymptotic properties of parametric estimators
62C99 Statistical decision theory
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