The Annals of Statistics

A Converse to Scheffe's Theorem

Dennis D. Boos

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Abstract

Convergence of densities implies convergence of their distribution functions via Scheffe's theorem. This paper is concerned with the converse: what are sufficient conditions to obtain convergence of densities from convergence of distribution functions? A general lemma is given and local limit results are obtained for translation and scale statistics.

Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 423-427.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346604

Digital Object Identifier
doi:10.1214/aos/1176346604

Mathematical Reviews number (MathSciNet)
MR773179

Zentralblatt MATH identifier
0567.62012

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G05: Estimation

Keywords
Convergence of densities local limit theorems translation statistics scale statistics

Citation

Boos, Dennis D. A Converse to Scheffe's Theorem. Ann. Statist. 13 (1985), no. 1, 423--427. doi:10.1214/aos/1176346604. https://projecteuclid.org/euclid.aos/1176346604


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