Simplical depth estimators and tests in examples from shape
analysis

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:

URL

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

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

Files attached

KatinaTMMP2008.pdf

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Citovat

KATINA, Stanislav, R. WELLMANN and Ch.H. MULLER. Simplical depth estimators and tests in examples from shape analysis. Tatra Mountains Mathematical Publications. Bratislava: Matematický ústav SAV, 2008, vol. 39, No 1, p. 95-104. ISSN 1210-3195.

@article{1067013,
   author = {Katina, Stanislav and Wellmann, R. and Muller, Ch.H.},
   article_location = {Bratislava},
   article_number = {1},
   keywords = {simplicial depth; maximum depth estimator; distribution-free tests; one-sample tests; two-sample tests; shape analysis; allometry},
   language = {eng},
   issn = {1210-3195},
   journal = {Tatra Mountains Mathematical Publications},
   title = {Simplical depth estimators and tests in examples from shape analysis},
   url = {http://tatra.mat.savba.sk/},
   volume = {39},
   year = {2008}
}

TY  - JOUR
ID  - 1067013
AU  - Katina, Stanislav - Wellmann, R. - Muller, Ch.H.
PY  - 2008
TI  - Simplical depth estimators and tests in examples from shape analysis
JF  - Tatra Mountains Mathematical Publications
VL  - 39
IS  - 1
SP  - 95-104
EP  - 95-104
PB  - Matematický ústav SAV
SN  - 12103195
KW  - simplicial depth
KW  - maximum depth estimator
KW  - distribution-free tests
KW  - one-sample tests
KW  - two-sample tests
KW  - shape analysis
KW  - allometry
UR  - http://tatra.mat.savba.sk/
N2  - 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.
ER  -

KATINA, Stanislav, R. WELLMANN and Ch.H. MULLER. Simplical depth estimators and tests in examples from shape analysis. \textit{Tatra Mountains Mathematical Publications}. Bratislava: Matematický ústav SAV, 2008, vol.~39, No~1, p.~95-104. ISSN~1210-3195.

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