Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle

The circular kernel density estimator, with the wrapped Cauchy kernel, is derived from the empirical version of Carathéodory function that is used in the literature on orthogonal polynomials on the unit circle. An equivalence between the resulting circular kernel density estimator, to Fourier series...

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Main Author: Yogendra P. Chaubey
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2018/5372803
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author Yogendra P. Chaubey
author_facet Yogendra P. Chaubey
author_sort Yogendra P. Chaubey
collection DOAJ
description The circular kernel density estimator, with the wrapped Cauchy kernel, is derived from the empirical version of Carathéodory function that is used in the literature on orthogonal polynomials on the unit circle. An equivalence between the resulting circular kernel density estimator, to Fourier series density estimator, has also been established. This adds further weight to the considerable role of the wrapped Cauchy distribution in circular statistics.
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spelling doaj-art-cc877bb22c774d97ba37f053e1193e2e2025-08-20T03:19:31ZengWileyJournal of Probability and Statistics1687-952X1687-95382018-01-01201810.1155/2018/53728035372803Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit CircleYogendra P. Chaubey0Department of Mathematics and Statistics, Concordia University, Montréal, QC, H3G 1M8, CanadaThe circular kernel density estimator, with the wrapped Cauchy kernel, is derived from the empirical version of Carathéodory function that is used in the literature on orthogonal polynomials on the unit circle. An equivalence between the resulting circular kernel density estimator, to Fourier series density estimator, has also been established. This adds further weight to the considerable role of the wrapped Cauchy distribution in circular statistics.http://dx.doi.org/10.1155/2018/5372803
spellingShingle Yogendra P. Chaubey
Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle
Journal of Probability and Statistics
title Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle
title_full Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle
title_fullStr Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle
title_full_unstemmed Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle
title_short Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle
title_sort smooth kernel estimation of a circular density function a connection to orthogonal polynomials on the unit circle
url http://dx.doi.org/10.1155/2018/5372803
work_keys_str_mv AT yogendrapchaubey smoothkernelestimationofacirculardensityfunctionaconnectiontoorthogonalpolynomialsontheunitcircle