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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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| 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. |
| format | Article |
| id | doaj-art-cc877bb22c774d97ba37f053e1193e2e |
| institution | DOAJ |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| 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 |