A Converse to Scheffe's Theorem

Dennis D. Boos

doi:10.1214/aos/1176346604

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Home > Journals > Ann. Statist. > Volume 13 > Issue 1 > Article

March, 1985 A Converse to Scheffe's Theorem

Dennis D. Boos

Ann. Statist. 13(1): 423-427 (March, 1985). DOI: 10.1214/aos/1176346604

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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.