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 a Ch.H. MULLER

Základní údaje

Originální název

Calculation of simplicial depth estimators for polynomial regression with applications

Autoři

WELLMANN, R.; Stanislav KATINA a Ch.H. MULLER

Vydání

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

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.029

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/07:00061104

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1016/j.csda.2006.10.015

UT WoS

000246681500019

Klíčová slova anglicky

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

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 21. 2. 2013 13:49, doc. PaedDr. RNDr. Stanislav Katina, Ph.D.

Anotace

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.

Návaznosti

CZ.1.07/2.2.00/15.0203, interní kód MU

Název: Univerzitní výuka matematiky v měnícím se světě (Akronym: Univerzitní výuka matematiky)

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Univerzitní výuka matematiky v měnícím se světě, 2.2 Vysokoškolské vzdělávání

Citovat

WELLMANN, R.; Stanislav KATINA a Ch.H. MULLER. Calculation of simplicial depth estimators for polynomial regression with applications. Computational Statistics & Data Analysis. Amsterdam: Elsevier, 2007, roč. 51, č. 10, s. 5025-5040. ISSN 0167-9473. Dostupné z: https://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 = {https://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 a Ch.H. MULLER. Calculation of simplicial depth estimators for polynomial regression with applications. \textit{Computational Statistics \&{} Data Analysis}. Amsterdam: Elsevier, 2007, roč.~51, č.~10, s.~5025-5040. ISSN~0167-9473. Dostupné z: https://doi.org/10.1016/j.csda.2006.10.015.

Přehled o publikaci