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Approximating exponential models. (English) Zbl 0721.62003

The authors describe Amari’s definition of locally approximating exponential models and provide some elementary properties and several examples of this type of approximation, which they call expected exponential approximation. The examples concern the von Mises distribution, nonlinear normal regression, and a simple model from quantum physics.
Similar to Amari’s, but in the framework of observed rather than expected, likelihood geometry they construct observed exponential approximations of a statistical model. Elementary properties of the resulting observed exponential approximations are discussed.
A more detailed discussion is given on the closeness of these approximations. The differences between the maximum likelihood estimators of the original model and the approximating models have the same convergence rate.
Reviewer: S.Zwanzig (Berlin)

MSC:

62A01 Foundations and philosophical topics in statistics
62F12 Asymptotic properties of parametric estimators
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