Some Linear Model Techniques for Analyzing Small Circle Spherical Data
The author investigates least squares as a method for fitting small circle models to a sample of unit vectors in R³. He highlights a local linear model underlying the estimation of the circle's parameters. This model is used to construct an estimation algorithm and regression type inference pro...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.46.6286 2023-05-15T16:05:41+02:00 Some Linear Model Techniques for Analyzing Small Circle Spherical Data Louis-Paul Rivest The Pennsylvania State University CiteSeerX Archives application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.6286 http://www.mat.ulaval.ca/cjs/pub/rivest/rivest.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.6286 http://www.mat.ulaval.ca/cjs/pub/rivest/rivest.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://www.mat.ulaval.ca/cjs/pub/rivest/rivest.pdf Key words and phrases Conical folds Directional data Fisher distribution Girdle distribution Rotationally symmetric distribution Spherical ellipse Watson distribution text ftciteseerx 2016-01-08T06:29:45Z The author investigates least squares as a method for fitting small circle models to a sample of unit vectors in R³. He highlights a local linear model underlying the estimation of the circle's parameters. This model is used to construct an estimation algorithm and regression type inference procedures for the circle's parameters. It makes it possible to compare the fit of a small circle with that of a spherical ellipse. The limitations of the least squares approach are emphasized: when the errors are bounded away from 0, the least squares estimators are not consistent as the sample size goes to infinity. Two examples, concerned with the migration of elephant seals and with the classification of geological folds, are analyzed using the linear model techniques proposed in this work. Text Elephant Seals Unknown |
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ftciteseerx |
language |
English |
topic |
Key words and phrases Conical folds Directional data Fisher distribution Girdle distribution Rotationally symmetric distribution Spherical ellipse Watson distribution |
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Key words and phrases Conical folds Directional data Fisher distribution Girdle distribution Rotationally symmetric distribution Spherical ellipse Watson distribution Louis-Paul Rivest Some Linear Model Techniques for Analyzing Small Circle Spherical Data |
topic_facet |
Key words and phrases Conical folds Directional data Fisher distribution Girdle distribution Rotationally symmetric distribution Spherical ellipse Watson distribution |
description |
The author investigates least squares as a method for fitting small circle models to a sample of unit vectors in R³. He highlights a local linear model underlying the estimation of the circle's parameters. This model is used to construct an estimation algorithm and regression type inference procedures for the circle's parameters. It makes it possible to compare the fit of a small circle with that of a spherical ellipse. The limitations of the least squares approach are emphasized: when the errors are bounded away from 0, the least squares estimators are not consistent as the sample size goes to infinity. Two examples, concerned with the migration of elephant seals and with the classification of geological folds, are analyzed using the linear model techniques proposed in this work. |
author2 |
The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
Louis-Paul Rivest |
author_facet |
Louis-Paul Rivest |
author_sort |
Louis-Paul Rivest |
title |
Some Linear Model Techniques for Analyzing Small Circle Spherical Data |
title_short |
Some Linear Model Techniques for Analyzing Small Circle Spherical Data |
title_full |
Some Linear Model Techniques for Analyzing Small Circle Spherical Data |
title_fullStr |
Some Linear Model Techniques for Analyzing Small Circle Spherical Data |
title_full_unstemmed |
Some Linear Model Techniques for Analyzing Small Circle Spherical Data |
title_sort |
some linear model techniques for analyzing small circle spherical data |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.6286 http://www.mat.ulaval.ca/cjs/pub/rivest/rivest.pdf |
genre |
Elephant Seals |
genre_facet |
Elephant Seals |
op_source |
http://www.mat.ulaval.ca/cjs/pub/rivest/rivest.pdf |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.6286 http://www.mat.ulaval.ca/cjs/pub/rivest/rivest.pdf |
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Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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1766401585615732736 |