Statistics
Merging information for a semiparametric projection density estimation
Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 331-335.

A semiparametric density estimator is proposed under a m-sample density ratio model, which specifies that the ratio of m1 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 m1 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.

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DOI: 10.1016/j.crma.2007.01.007
Aubin, Jean-Baptiste 1; Leoni-Aubin, Samuela 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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Aubin, Jean-Baptiste; Leoni-Aubin, Samuela. 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. http://www.numdam.org/articles/10.1016/j.crma.2007.01.007/

[1] Aubin, J.B.; Massiani, A. Comportement asymptotique d'un estimateur de la densité adaptatif par méthode d'ondelettes, C. R. Acad. Sci. Paris, Ser. I, Volume 337 (2003) no. 4, pp. 293-296

[2] Bosq, D. Estimation localement suroptimale et adaptative de la densité, C. R. Acad. Sci. Paris, Ser. I, Volume 334 (2002) no. 7, pp. 591-595

[3] Bosq, D. Inférence et prévision en grandes dimensions, Economica, 2005

[4] Cencov, N.N. Estimation of unknown distribution density from observations, Soviet Math. Dokl., Volume 3 (1962), pp. 1559-1562

[5] Cheng, K.F.; Chu, C.K. Semiparametric density estimation under a two-sample density ratio model, Bernoulli, Volume 10 (2004) no. 4, pp. 583-604

[6] Fokianos, K. Merging information for semiparametric density estimation, Part 4, J. R. Statist. Soc. B, Volume 66 (2004), pp. 941-958

[7] Fokianos, K.; Kedem, B.; Qin, J.; Haferman, J.; Short, D.A. On combining instruments, J. Appl. Meteorology, Volume 37 (1998), pp. 220-226

[8] Fokianos, K.; Kedem, B.; Qin, J.; Short, D.A. A semiparametric approach to the one-way layout, Technometrics, Volume 43 (2001), pp. 56-64

[9] Keziou, A.; Leoni-Aubin, S. Test of homogeneity in semiparametric two-sample density ratio models, C. R. Acad. Sci. Paris, Ser. I, Volume 340 (2005) no. 12, pp. 905-910

[10] Owen, A.B. Empirical likelihood ratio confidence intervals for a single functional, Biometrika, Volume 75 (1988) no. 2, pp. 237-249

[11] Owen, A.B. Empirical Likelihood, Chapman and Hall, New York, 2001

[12] Picard, D.; Tribouley, K. Adaptive confidence interval for pointwise curve estimation, Ann. Statist., Volume 28 (2000) no. 1, pp. 298-335

[13] Qin, J. Inferences for case-control and semiparametric two-sample density ratio models, Biometrika, Volume 85 (1998) no. 3, pp. 619-630

[14] Qin, J.; Lawless, J. Empirical likelihood and general estimating equations, Ann. Statist., Volume 22 (1994) no. 1, pp. 300-325

[15] Qin, B.; Zhang, J. Density estimation under a two-sample semiparametric model, Nonparametr. Statist., Volume 17 (2005) no. 6, pp. 665-683

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