Testing hypotheses on independent, not identically distributed models

Wolfgang Wefelmeyer
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Wolfgang Wefelmeyer: University of Cologne, Mathematical Institute

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 267-282 from Springer

Abstract: 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.

Keywords: Probability Measure; Asymptotic Normality; Hausdorff Distance; Independent Model; Asymptotic Level (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_20

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DOI: 10.1007/978-94-009-3963-9_20

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