A projection method of estimation for a subfamily of exponential families (Q1819849)
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scientific article; zbMATH DE number 3994746
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A projection method of estimation for a subfamily of exponential families |
scientific article; zbMATH DE number 3994746 |
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A projection method of estimation for a subfamily of exponential families (English)
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1986
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In the estimation for a subfamily of exponential type, the author defines a projection estimator, using the orthogonal projection of the transformed statistic onto the flat surface which is connected with a distance by \textit{P. C. Mahalanobis} [Proc. Natl. Inst. Sci. India 2, 49-55 (1936; Zbl 0015.03302)]. He shows the asymptotic normality of the projection estimator, hence obtains its first-order efficiency. It is also shown that the projection estimator is not generally second-order efficient, but the one-step maximum likelihood estimator from the projection estimator is second-order efficient. Some examples are given.
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sufficient statistic
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Mahalanobis distance
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ABO blood group model
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exponential family
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projection estimator
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asymptotic normality
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first-order efficiency
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one-step maximum likelihood estimator
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second-order efficient
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