Regression Modeling for Spherical Data via Non-parametric and Least Square Methods
Introduction Statistical analysis of the data on the Earth's surface was a favorite subject among many researchers. Such data can be related to animal's migration from a region to another position. Then, statistical modeling of their paths helps biological researchers to predict their move...
Main Authors: | , |
---|---|
Format: | Article in Journal/Newspaper |
Language: | Persian |
Published: |
Kharazmi University
2019
|
Subjects: | |
Online Access: | https://doaj.org/article/d6e691342fac49a4be194ad0cc33106f |
id |
ftdoajarticles:oai:doaj.org/article:d6e691342fac49a4be194ad0cc33106f |
---|---|
record_format |
openpolar |
spelling |
ftdoajarticles:oai:doaj.org/article:d6e691342fac49a4be194ad0cc33106f 2023-05-15T18:23:21+02:00 Regression Modeling for Spherical Data via Non-parametric and Least Square Methods mosa golalizadeh m moghimbeigy 2019-08-01T00:00:00Z https://doaj.org/article/d6e691342fac49a4be194ad0cc33106f FA per Kharazmi University http://mmr.khu.ac.ir/article-1-2565-en.html https://doaj.org/toc/2588-2546 https://doaj.org/toc/2588-2554 2588-2546 2588-2554 https://doaj.org/article/d6e691342fac49a4be194ad0cc33106f پژوهشهای ریاضی, Vol 5, Iss 1, Pp 85-94 (2019) risk function spherical data non-parametric regression longitudinal model Mathematics QA1-939 article 2019 ftdoajarticles 2023-03-19T01:32:16Z Introduction Statistical analysis of the data on the Earth's surface was a favorite subject among many researchers. Such data can be related to animal's migration from a region to another position. Then, statistical modeling of their paths helps biological researchers to predict their movements and estimate the areas that are most likely to constitute the presence of the animals. From a geometrical view, spherical data are points that take their values on the surface of a unit sphere. There are many methods to fit a curve, especially regression curves to spherical data. For example, Gould [1] used the corresponding angles of spherical data coordinates to introduce regression models. He considered Fisher distribution as a candidate density for the error in his analysis. A non-parametric version of his model was proposed by Thompson and Clark [2]. Usually, the data that are close to the North or South pole have different behavior. Hence, their proposed model was failing to work there, and so they tried to keep the data somewhat away from the pole via adopting their model. They advocated overcoming this problem by using the tangent plane and suggested the use of splines there [3]. On the other hand, Fisher et al. [4] proposed two families of the spherical spline for spherical data. They introduced two families of curves using differential geometry suitable for fitting the splines. One of the methods to predict statistics is to utilize non-parametric regression models. Another strategy is to consider some forms of smooth models. Both of these procedures, along with other approaches in non-Euclidean statistics context are somewhat an initiative method in analyzing the spherical data. It worths mentioning that the benefits of using the spline path by employing the rotation parameters were of interest in directional statistics in [5], albeit for circular data. One of the interesting techniques to construct the non-parametric regression model was to minimize the Euclidean risk function, first proposed in [6]. We also ... Article in Journal/Newspaper South pole Directory of Open Access Journals: DOAJ Articles South Pole |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
Persian |
topic |
risk function spherical data non-parametric regression longitudinal model Mathematics QA1-939 |
spellingShingle |
risk function spherical data non-parametric regression longitudinal model Mathematics QA1-939 mosa golalizadeh m moghimbeigy Regression Modeling for Spherical Data via Non-parametric and Least Square Methods |
topic_facet |
risk function spherical data non-parametric regression longitudinal model Mathematics QA1-939 |
description |
Introduction Statistical analysis of the data on the Earth's surface was a favorite subject among many researchers. Such data can be related to animal's migration from a region to another position. Then, statistical modeling of their paths helps biological researchers to predict their movements and estimate the areas that are most likely to constitute the presence of the animals. From a geometrical view, spherical data are points that take their values on the surface of a unit sphere. There are many methods to fit a curve, especially regression curves to spherical data. For example, Gould [1] used the corresponding angles of spherical data coordinates to introduce regression models. He considered Fisher distribution as a candidate density for the error in his analysis. A non-parametric version of his model was proposed by Thompson and Clark [2]. Usually, the data that are close to the North or South pole have different behavior. Hence, their proposed model was failing to work there, and so they tried to keep the data somewhat away from the pole via adopting their model. They advocated overcoming this problem by using the tangent plane and suggested the use of splines there [3]. On the other hand, Fisher et al. [4] proposed two families of the spherical spline for spherical data. They introduced two families of curves using differential geometry suitable for fitting the splines. One of the methods to predict statistics is to utilize non-parametric regression models. Another strategy is to consider some forms of smooth models. Both of these procedures, along with other approaches in non-Euclidean statistics context are somewhat an initiative method in analyzing the spherical data. It worths mentioning that the benefits of using the spline path by employing the rotation parameters were of interest in directional statistics in [5], albeit for circular data. One of the interesting techniques to construct the non-parametric regression model was to minimize the Euclidean risk function, first proposed in [6]. We also ... |
format |
Article in Journal/Newspaper |
author |
mosa golalizadeh m moghimbeigy |
author_facet |
mosa golalizadeh m moghimbeigy |
author_sort |
mosa golalizadeh |
title |
Regression Modeling for Spherical Data via Non-parametric and Least Square Methods |
title_short |
Regression Modeling for Spherical Data via Non-parametric and Least Square Methods |
title_full |
Regression Modeling for Spherical Data via Non-parametric and Least Square Methods |
title_fullStr |
Regression Modeling for Spherical Data via Non-parametric and Least Square Methods |
title_full_unstemmed |
Regression Modeling for Spherical Data via Non-parametric and Least Square Methods |
title_sort |
regression modeling for spherical data via non-parametric and least square methods |
publisher |
Kharazmi University |
publishDate |
2019 |
url |
https://doaj.org/article/d6e691342fac49a4be194ad0cc33106f |
geographic |
South Pole |
geographic_facet |
South Pole |
genre |
South pole |
genre_facet |
South pole |
op_source |
پژوهشهای ریاضی, Vol 5, Iss 1, Pp 85-94 (2019) |
op_relation |
http://mmr.khu.ac.ir/article-1-2565-en.html https://doaj.org/toc/2588-2546 https://doaj.org/toc/2588-2554 2588-2546 2588-2554 https://doaj.org/article/d6e691342fac49a4be194ad0cc33106f |
_version_ |
1766202921410625536 |