On convergence of densities of translation and scale statistics.
Dennis D. Boos · NCSU Libraries Repository (North Carolina State University Libraries) · 1983
Convergence of densities leads directly to 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 results are obtained for translation and scale statistics with applications to bootstrap estimates of densities and convergence of Bayes posteriors.