Calculation of simplicial depth estimators for polynomial
regression with applications

J 2007

Calculation of simplicial depth estimators for polynomial regression with applications

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

Basic information

Original name

Calculation of simplicial depth estimators for polynomial regression with applications

Authors

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

Edition

Computational Statistics & Data Analysis, Amsterdam, Elsevier, 2007, 0167-9473

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Ireland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL

Impact factor

Impact factor: 1.029

RIV identification code

RIV/00216224:14310/07:00061104

Organization unit

Faculty of Science

DOI

http://dx.doi.org/10.1016/j.csda.2006.10.015

UT WoS

000246681500019

Keywords in English

Polynomial regression; Simplicial depth; Maximum depth estimator; Distribution free tests; One-sample tests; Two-sample tests; Shape analysis

Abstract

V originále

A fast algorithm for calculating the simplicial depth of a single parameter vector of a polynomial regression model is derived. Additionally, an algorithm for calculating the parameter vectors with maximum simplicial depth within an affine subspace of the parameter space or a polyhedron is presented. Since the maximum simplicial depth estimator is not unique, l1 and l2 methods are used to make the estimator unique. This estimator is compared with other estimators in examples of linear and quadratic regression. Furthermore, it is shown how the maximum simplicial depth can be used to derive distribution-free asymptotic alpha-level tests for testing hypotheses in polynomial regression models. The tests are applied on a problem of shape analysis where it is tested how the relative head length of the fish species Lepomis gibbosus depends on the size of these fishes. It is also tested whether the dependency can be described by the same polynomial regression function within different populations.

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

Citovat

WELLMANN, R., Stanislav KATINA and Ch.H. MULLER. Calculation of simplicial depth estimators for polynomial regression with applications. Computational Statistics & Data Analysis. Amsterdam: Elsevier, 2007, vol. 51, No 10, p. 5025-5040. ISSN 0167-9473. Available from: https://dx.doi.org/10.1016/j.csda.2006.10.015.

@article{1067017,
   author = {Wellmann, R. and Katina, Stanislav and Muller, Ch.H.},
   article_location = {Amsterdam},
   article_number = {10},
   doi = {http://dx.doi.org/10.1016/j.csda.2006.10.015},
   keywords = {Polynomial regression; Simplicial depth; Maximum depth estimator; Distribution free tests; One-sample tests; Two-sample tests; Shape analysis},
   language = {eng},
   issn = {0167-9473},
   journal = {Computational Statistics & Data Analysis},
   title = {Calculation of simplicial depth estimators for polynomial regression with applications},
   url = {http://www.sciencedirect.com/science/article/pii/S0167947306003847},
   volume = {51},
   year = {2007}
}

TY  - JOUR
ID  - 1067017
AU  - Wellmann, R. - Katina, Stanislav - Muller, Ch.H.
PY  - 2007
TI  - Calculation of simplicial depth estimators for polynomial regression with applications
JF  - Computational Statistics & Data Analysis
VL  - 51
IS  - 10
SP  - 5025-5040
EP  - 5025-5040
PB  - Elsevier
SN  - 01679473
KW  - Polynomial regression
KW  - Simplicial depth
KW  - Maximum depth estimator
KW  - Distribution free tests
KW  - One-sample tests
KW  - Two-sample tests
KW  - Shape analysis
UR  - http://www.sciencedirect.com/science/article/pii/S0167947306003847
N2  - A fast algorithm for calculating the simplicial depth of a single parameter vector of a polynomial regression model is derived. Additionally, an algorithm for calculating the parameter vectors with maximum simplicial depth within an affine subspace of the parameter space or a polyhedron is presented. Since the maximum simplicial depth estimator is not unique, l1 and l2 methods are used to make the estimator unique. This estimator is compared with other estimators in examples of linear and quadratic regression. Furthermore, it is shown how the maximum simplicial depth can be used to derive distribution-free asymptotic alpha-level tests for testing hypotheses in polynomial regression models. The tests are applied on a problem of shape analysis where it is tested how the relative head length of the fish species Lepomis gibbosus depends on the size of these fishes. It is also tested whether the dependency can be described by the same polynomial regression function within different populations.
ER  -

WELLMANN, R., Stanislav KATINA and Ch.H. MULLER. Calculation of simplicial depth estimators for polynomial regression with applications. \textit{Computational Statistics \&{} Data Analysis}. Amsterdam: Elsevier, 2007, vol.~51, No~10, p.~5025-5040. ISSN~0167-9473. Available from: https://dx.doi.org/10.1016/j.csda.2006.10.015.

Detailed Information on Publication Record