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A projection method of estimation for a subfamily of exponential families. (English) Zbl 0614.62028

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 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.
Reviewer: M.Akahira

MSC:

62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62J05 Linear regression; mixed models
62P10 Applications of statistics to biology and medical sciences; meta analysis

Citations:

Zbl 0015.03302
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References:

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