Merging information for a semiparametric projection density estimation

Jean-Baptiste Aubin; Samuela Leoni-Aubin

doi:10.1016/j.crma.2007.01.007

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Merging information for a semiparametric projection density estimation

Presented by: Paul Deheuvels

Jean-Baptiste Aubin ¹; Samuela Leoni-Aubin ¹

¹ Université de technologie de Compiègne, centre de recherches de Royallieu, rue Personne de Roberval, BP 20529, 60205 Compiègne, France

Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 331-335.

Abstract
Résumé

A semiparametric density estimator is proposed under a m-sample density ratio model, which specifies that the ratio of $m - 1$ probability density functions with respect to the mth is of a known parametric form without reference to any parametric model. This model arises naturally from retrospective studies and multinomial logistic regression model. A projection density estimator is constructed by smoothing the increments of the maximum semiparametric likelihood estimator of the underlying distribution function, using the combined data from all the samples. We also establish some asymptotic results on the proposed projection density estimator.

On propose un estimateur semiparamétrique de la densité dans le contexte d'un modèle à rapport de densités à m échantillons. Ce dernier spécifie que les rapports des $m - 1$ premières densités par rapport à la dernière sont de forme paramétrique connue. Ce modèle est adapté à des études de type rétrospectif et inclut le cas de la régression logistique multinomial. Nous étudions le problème d'inférence semiparamétrique lié au modèle à rapport de densités en utilisant la méthode de la vraisemblance empirique. Nous utilisons les données combinées des m échantillons afin de calculer un nouvel estimateur adaptatif par projection des densités inconnues.

Received: 2006-10-10
Accepted: 2007-01-10
Published online: 2007-02-12

DOI: 10.1016/j.crma.2007.01.007

Author's affiliations:

Jean-Baptiste Aubin ¹; Samuela Leoni-Aubin ¹

¹ Université de technologie de Compiègne, centre de recherches de Royallieu, rue Personne de Roberval, BP 20529, 60205 Compiègne, France

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     title = {Merging information for a semiparametric projection density estimation},
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     doi = {10.1016/j.crma.2007.01.007},
     language = {en},
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Jean-Baptiste Aubin; Samuela Leoni-Aubin. Merging information for a semiparametric projection density estimation. Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 331-335. doi : 10.1016/j.crma.2007.01.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.01.007/

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