J 2008

Simplical depth estimators and tests in examples from shape analysis

KATINA, Stanislav, R. WELLMANN and Ch.H. MULLER

Basic information

Original name

Simplical depth estimators and tests in examples from shape analysis

Authors

KATINA, Stanislav (703 Slovakia, guarantor, belonging to the institution), R. WELLMANN (276 Germany) and Ch.H. MULLER (276 Germany)

Edition

Tatra Mountains Mathematical Publications, Bratislava, Matematický ústav SAV, 2008, 1210-3195

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10103 Statistics and probability

Country of publisher

Slovakia

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

RIV identification code

RIV/00216224:14310/08:00061100

Organization unit

Faculty of Science

UT WoS

000260473000010

Keywords in English

simplicial depth; maximum depth estimator; distribution-free tests; one-sample tests; two-sample tests; shape analysis; allometry

Tags

Tags

International impact, Reviewed
Změněno: 21/2/2013 13:25, doc. PaedDr. RNDr. Stanislav Katina, Ph.D.

Abstract

V originále

In this paper we present the maximum simplicial depth estimator and compare it to the ordinary least square estimator in examples from 2D and 3D shape analysis focusing on bivariate and multivariate allometrical problems from zoology and biological anthropology. We compare two types of estimators derived under different subsets of parametric space on the basis of the linear regression model, theta = (theta1, theta2)T in R2 and theta = (theta1, theta2, theta3)T in R3, where theta3 = 0. We also discuss monotonically decreasing linear regression models in special situations. In applications where outliers in x- or y-axis direction occur in the data and residuals from ordinary least-square linear regression model are not normally distributed, we recommend the use of the maximum simplicial depth estimators.

Links

CZ.1.07/2.2.00/15.0203, interní kód MU
Name: Univerzitní výuka matematiky v měnícím se světě (Acronym: Univerzitní výuka matematiky)
Investor: Ministry of Education, Youth and Sports of the CR, 2.2 Higher education

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