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September, 1986 On a Converse to Scheffe's Theorem
T. J. Sweeting
Ann. Statist. 14(3): 1252-1256 (September, 1986). DOI: 10.1214/aos/1176350065

Abstract

In Boos (1985) equicontinuity conditions are given which ensure the uniform convergence of densities in $\mathbb{R}^k$, given convergence in distribution. In the present note we show that such equicontinuity conditions in fact characterize uniform local convergence with no additional assumptions on the sequence of densities, or on the limit density. Versions of these results are also given when the distributions depend on an unknown parameter; these forms will be relevant for the uniform approximation of likelihood functions.

Citation

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T. J. Sweeting. "On a Converse to Scheffe's Theorem." Ann. Statist. 14 (3) 1252 - 1256, September, 1986. https://doi.org/10.1214/aos/1176350065

Information

Published: September, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0605.62010
MathSciNet: MR856821
Digital Object Identifier: 10.1214/aos/1176350065

Subjects:
Primary: 62E20
Secondary: 60F99

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 3 • September, 1986
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