[De nouveaux développements de Karhunen-Loève basés sur les polynômes de Hahn avec application à un test d’uniformité de Sobolev sur les graphes de Johnson]
Nous proposons un nouveau développement de Karhunen-Loève avec les polynômes de Hahn. Cela nous permet d’introduire une analogue discrète de la statistique de Watson pour tester l’uniformité d’une distribution sur les graphes de Johnson, dont les fontions sphériques zonales sont les polynômes de Hahn. Ce test peut être vu comme un test de Sobolev dans le cas discret, nous en déduisons certaines de ses propriétés asymptotiques.
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.
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Keywords: Karhunen-Loève expansions, classical orthogonal polynomials, distance regular graphs, directional statistics
Mot clés : développements de Karhunen-Loève, polynômes orthogonaux classiques, Graphes distance-réguliers, statistiques directionnelles
Jean-Renaud Pycke 1
CC-BY 4.0
@article{CRMATH_2024__362_G7_701_0,
author = {Jean-Renaud Pycke},
title = {New {Karhunen-Lo\`eve} expansions based on {Hahn} polynomials with application to a {Sobolev} test for uniformity on {Johnson} graphs},
journal = {Comptes Rendus. Math\'ematique},
pages = {701--711},
publisher = {Acad\'emie des sciences, Paris},
volume = {362},
year = {2024},
doi = {10.5802/crmath.470},
language = {en},
}
TY - JOUR AU - Jean-Renaud Pycke TI - New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs JO - Comptes Rendus. Mathématique PY - 2024 SP - 701 EP - 711 VL - 362 PB - Académie des sciences, Paris DO - 10.5802/crmath.470 LA - en ID - CRMATH_2024__362_G7_701_0 ER -
%0 Journal Article %A Jean-Renaud Pycke %T New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs %J Comptes Rendus. Mathématique %D 2024 %P 701-711 %V 362 %I Académie des sciences, Paris %R 10.5802/crmath.470 %G en %F CRMATH_2024__362_G7_701_0
Jean-Renaud Pycke. New Karhunen-Loève expansions based on Hahn polynomials with application to a Sobolev test for uniformity on Johnson graphs. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 701-711. doi : 10.5802/crmath.470. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.470/
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