New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs
We give a new family of Karhunen-Loève expansions involving Hahn polynomials. This enables us to introduce discrete analogues of Watson statistics, and a test for uniformity on Johnson’s graphs. We use the fact that the zonal spherical functions on these graphs are Hahn polynomials. Our test is cons...
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| Language: | English |
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Académie des sciences
2024-09-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.470/ |
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| author | Pycke, Jean-Renaud |
| author_facet | Pycke, Jean-Renaud |
| author_sort | Pycke, Jean-Renaud |
| collection | DOAJ |
| description | We give a new family of Karhunen-Loève expansions involving Hahn polynomials. This enables us to introduce discrete analogues of Watson statistics, and a test for uniformity on Johnson’s graphs. We use the fact that the zonal spherical functions on these graphs are Hahn polynomials. Our test is consistent against all alternatives and locally most powerful against some alternative. |
| format | Article |
| id | doaj-art-a8770b59327b4e7db18da07bd68a2825 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-a8770b59327b4e7db18da07bd68a28252025-02-07T11:22:28ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-09-01362G770171110.5802/crmath.47010.5802/crmath.470New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphsPycke, Jean-Renaud0LaMME CNRS (UMR 8071), University of Paris-Saclay (Evry), FranceWe give a new family of Karhunen-Loève expansions involving Hahn polynomials. This enables us to introduce discrete analogues of Watson statistics, and a test for uniformity on Johnson’s graphs. We use the fact that the zonal spherical functions on these graphs are Hahn polynomials. Our test is consistent against all alternatives and locally most powerful against some alternative.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.470/Karhunen-Loève expansionsclassical orthogonal polynomialsdistance regular graphsdirectional statistics |
| spellingShingle | Pycke, Jean-Renaud New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs Comptes Rendus. Mathématique Karhunen-Loève expansions classical orthogonal polynomials distance regular graphs directional statistics |
| title | New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs |
| title_full | New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs |
| title_fullStr | New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs |
| title_full_unstemmed | New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs |
| title_short | New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs |
| title_sort | new karhunen loeve expansions based on hahn polynomials with application to a sobolev test for uniformity on johnson graphs |
| topic | Karhunen-Loève expansions classical orthogonal polynomials distance regular graphs directional statistics |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.470/ |
| work_keys_str_mv | AT pyckejeanrenaud newkarhunenloeveexpansionsbasedonhahnpolynomialswithapplicationtoasobolevtestforuniformityonjohnsongraphs |