A Converse to Scheffe's Theorem
Open Access
- 1 March 1985
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 13 (1) , 423-427
- https://doi.org/10.1214/aos/1176346604
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.Keywords
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