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June, 1986 The Statistical Information Contained in Additional Observations
Enno Mammen
Ann. Statist. 14(2): 665-678 (June, 1986). DOI: 10.1214/aos/1176349945

Abstract

Let $\mathscr{E}^n$ be a statistical experiment based on $n$ i.i.d. observations. We compare $\mathscr{E}^n$ with $\mathscr{E}^{n+r_n}$. The gain of information due to the $r_n$ additional observations is measured by the deficiency distance $\Delta (\mathscr{E}^n, \mathscr{E}^{n+r_n})$, i.e., the maximum diminution of the risk functions. We show that under general dimensionality conditions $\Delta(\mathscr{E}^n, \mathscr{E}^{n+r_n})$ is of order $r_n/n$. Further the behavior of $\Delta$ is studied and compared for asymptotically Gaussian experiments. We show that the information gain increases logarithmically. The Gaussian and the binomial family turn out to be--in some sense--opposite extreme cases, with the increase of information asymptotically minimal in the Gaussian case and maximal in the binomial.

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Enno Mammen. "The Statistical Information Contained in Additional Observations." Ann. Statist. 14 (2) 665 - 678, June, 1986. https://doi.org/10.1214/aos/1176349945

Information

Published: June, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0633.62006
MathSciNet: MR840521
Digital Object Identifier: 10.1214/aos/1176349945

Subjects:
Primary: 62B15

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 2 • June, 1986
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