### 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 language | English |
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Pages (from-to) | 3003-3012 |

Journal | Journal of Statistical Planning and Inference |

Volume | 140 |

Issue number | 11 |

Publication status | Published - 2010 |

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## Cite this

Einmahl, J. H. J., Gantner, M., & Sawitzki, G. (2010). Asymptotics of the Shorth Plot.

*Journal of Statistical Planning and Inference*,*140*(11), 3003-3012.