# The Shorth Plot

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

Research output: Working paperDiscussion paperOther research output

### 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.
Original language English Tilburg Econometrics 24 2008-24 Published - 2008

### Publication series

Name CentER Discussion Paper 2008-24

### Fingerprint

Functional Central Limit Theorem
Bandwidth Selection
Short Intervals
Graphical Representation
Forcing
Scanning
Sample Size
Rate of Convergence
Covering
Probability Distribution
Interval

### Keywords

• Data analysis
• distribution diagnostics
• functional central limit theorem
• probability mass concentration

### Cite this

Einmahl, J. H. J., Gantner, M., & Sawitzki, G. (2008). The Shorth Plot. (CentER Discussion Paper; Vol. 2008-24). Tilburg: Econometrics.
Einmahl, J.H.J. ; Gantner, M. ; Sawitzki, G. / The Shorth Plot. Tilburg : Econometrics, 2008. (CentER Discussion Paper).
@techreport{10b5cfb5c50246dc8e515481cf47f6d9,
title = "The Shorth Plot",
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",
author = "J.H.J. Einmahl and M. Gantner and G. Sawitzki",
note = "Subsequently published in Journal of Computational and Geographical Statistics, 2010 Pagination: 24",
year = "2008",
language = "English",
volume = "2008-24",
series = "CentER Discussion Paper",
publisher = "Econometrics",
type = "WorkingPaper",
institution = "Econometrics",

}

Einmahl, JHJ, Gantner, M & Sawitzki, G 2008 'The Shorth Plot' CentER Discussion Paper, vol. 2008-24, Econometrics, Tilburg.

The Shorth Plot. / Einmahl, J.H.J.; Gantner, M.; Sawitzki, G.

Tilburg : Econometrics, 2008. (CentER Discussion Paper; Vol. 2008-24).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - The Shorth Plot

AU - Einmahl, J.H.J.

AU - Gantner, M.

AU - Sawitzki, G.

N1 - Subsequently published in Journal of Computational and Geographical Statistics, 2010 Pagination: 24

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Data analysis

KW - distribution diagnostics

KW - functional central limit theorem

KW - probability mass concentration

M3 - Discussion paper

VL - 2008-24

T3 - CentER Discussion Paper

BT - The Shorth Plot

PB - Econometrics

CY - Tilburg

ER -

Einmahl JHJ, Gantner M, Sawitzki G. The Shorth Plot. Tilburg: Econometrics. 2008. (CentER Discussion Paper).