Calculation of simplicial depth estimators for polynomial regression with applications

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Publikace nespadá pod Filozofickou fakultu, ale pod Přírodovědeckou fakultu. Oficiální stránka publikace je na webu muni.cz.
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WELLMANN R. KATINA Stanislav MULLER Ch.H.

Rok publikování 2007
Druh Článek v odborném periodiku
Časopis / Zdroj Computational Statistics & Data Analysis
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
www http://www.sciencedirect.com/science/article/pii/S0167947306003847
Doi http://dx.doi.org/10.1016/j.csda.2006.10.015
Obor Obecná matematika
Klíčová slova Polynomial regression; Simplicial depth; Maximum depth estimator; Distribution free tests; One-sample tests; Two-sample tests; Shape analysis
Popis 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.
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