Asymptotics of the Shorth Plot

J.H.J. Einmahl, M. Gantner, G. Sawitzki

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

Abstract

The shorth plot is a nonparametric method to visualize probability mass concentration. It is based on the length of the shortest interval containing a certain fraction of the probability distribution and a point x. We establish functional central limit theorems (convergence rate 1/√n ) for the empirical shorth plot under natural conditions. The limiting process is not necessarily Gaussian. In the proofs, we generalize the Vervaat (1972) lemma to a collection of functions.
Original languageEnglish
Pages (from-to)3003-3012
JournalJournal of Statistical Planning and Inference
Volume140
Issue number11
Publication statusPublished - 2010

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