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Testing hypotheses on independent, not identically distributed models

In: Mathematical Statistics and Probability Theory

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  • Wolfgang Wefelmeyer

    (University of Cologne, Mathematical Institute)

Abstract

A family of probability measures can be identified with a subset of the Hilbert space generated by the Hellinger distance. The family is smooth at a fixed probability measure if the corresponding subset admits a tangent space with respect to the Hausdorff distance at the point corresponding to the fixed probability measure. This smoothness concept was introduced by Chernoff and LeCam. An asymptotic version can be defined for hypotheses on independent, not necessarily identically distributed observations. Assuming that the hypothesis is asymptotically smooth in this sense, we obtain an asymptotic bound for the power of tests under contiguous alternatives. The bound is sharp. If a test-sequence attains the bound for a single alternative, its asymptotic power is uniquely determined.

Suggested Citation

  • Wolfgang Wefelmeyer, 1987. "Testing hypotheses on independent, not identically distributed models," Springer Books, in: M. L. Puri & P. Révész & W. Wertz (ed.), Mathematical Statistics and Probability Theory, pages 267-282, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-3963-9_20
    DOI: 10.1007/978-94-009-3963-9_20
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