Calculation of simplicial depth estimators for polynomial regression with applications

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Calculation of simplicial depth estimators for polynomial regression with applications
Original language description
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
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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