A Converse to Scheffe's Theorem
The Annals of Statistics · 1985 · Volume 13 · Issue 1
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
62E20, 62G05, Convergence of densities, Local limit theorems, scale statistics, translation statistics
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