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The Shorth Plot

CentER Discussion Paper No. 2008-24

24 Pages Posted: 21 Feb 2008  

John H. J. Einmahl

Tilburg University - Department of Econometrics & Operations Research

Maria Gantner

Tilburg University - Center and Faculty of Economics and Business Administration

Günther Sawitzki

University of Heidelberg - StatLab Heidelberg

Date Written: February 2008

Abstract

The shorth plot is a tool to investigate probability mass concentration. It is a graphical representation of the length of the shorth, the shortest interval covering a certain fraction of the distribution, localized by forcing the intervals considered to contain a given point x. It is easy to compute, avoids bandwidth selection problems and allows scanning for local as well as for global features of the probability distribution. We prove functional central limit theorems for the empirical shorth plot. The good rate of convergence of the empirical shorth plot makes it useful already for moderate sample size.

Keywords: Data analysis, distribution diagnostics, functional central limit theorem, probability mass concentration

JEL Classification: C13, C14

Suggested Citation

Einmahl, John H. J. and Gantner, Maria and Sawitzki, Günther, The Shorth Plot (February 2008). CentER Discussion Paper No. 2008-24. Available at SSRN: https://ssrn.com/abstract=1096058 or http://dx.doi.org/10.2139/ssrn.1096058

John H. J. Einmahl (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

P.O. Box 90153
5000 LE Tilburg
Netherlands

Maria Gantner

Tilburg University - Center and Faculty of Economics and Business Administration ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Günther Sawitzki

University of Heidelberg - StatLab Heidelberg ( email )

Im Neuenheimer Feld 294
Heidelberg, 69120
Germany

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