Calculation of simplicial depth estimators for polynomial regression with applications

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F07%3A00061104" target="_blank" >RIV/00216224:14310/07:00061104 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.csda.2006.10.015" target="_blank" >http://dx.doi.org/10.1016/j.csda.2006.10.015</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.csda.2006.10.015" target="_blank" >10.1016/j.csda.2006.10.015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Calculation of simplicial depth estimators for polynomial regression with applications

Popis výsledku v původním jazyce

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 populati

Název v anglickém jazyce

Calculation of simplicial depth estimators for polynomial regression with applications

Popis výsledku anglicky

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 populati

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

R - Projekt Ramcoveho programu EK

Rok uplatnění

2007

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computational Statistics & Data Analysis

ISSN

0167-9473

e-ISSN

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Svazek periodika

51

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

IE - Irsko

Počet stran výsledku

16

Strana od-do

5025-5040

Kód UT WoS článku

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EID výsledku v databázi Scopus

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