Summary
Under certain regularity conditions products E n of an experiment E can be locally approximated by homoschedastic Gaussian experiments G n. G n can be defined such that the square roots of the densities have nearly the same structure with respect to the L 2-geometry as in E n. The main result of this paper is that this choice of G n is asymptotically optimal in the sense of minimizing the deficiency distance between E n and G if E is a one-dimensional exponential family.
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This work has been supported by the Deutsche Forschungsgemeinschaft
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Mammen, E. Optical local Gaussian approximation of an exponential family. Probab. Th. Rel. Fields 76, 103–119 (1987). https://doi.org/10.1007/BF00390278
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DOI: https://doi.org/10.1007/BF00390278