[Distribution estimation from biased data with unknown weighting function]
We consider the problem of estimating the cumulative distribution function (cdf) G of a non-negative random variable (r.v.) X from the observation of a biased r.v. Y with cdf , where w is an unknown weighting function. We assume moreover that the random sample with common cdf is right-censored. We construct an estimator for the cdf G and state its strong consistency and weak convergence.
Nous considérons le problème de l'estimation de la fonction de répartition G d'une variable aléatoire (v.a.) positive X à partir de l'observation d'une v.a. biaisée Y de fonction de répartition , où w est une fonction de poids inconnue. En supposant de plus que l'échantillon issu de la fonction de répartition est censuré à droite, nous construisons un estimateur de la fonction de répartition G pour lequel on énonce un théorème de consistance forte et de convergence faible.
Accepted:
Published online:
Agathe Guilloux 1
@article{CRMATH_2006__342_4_275_0, author = {Agathe Guilloux}, title = {Estimation sous biais de s\'election et avec fonction de poids inconnue}, journal = {Comptes Rendus. Math\'ematique}, pages = {275--278}, publisher = {Elsevier}, volume = {342}, number = {4}, year = {2006}, doi = {10.1016/j.crma.2005.11.016}, language = {fr}, }
Agathe Guilloux. Estimation sous biais de sélection et avec fonction de poids inconnue. Comptes Rendus. Mathématique, Volume 342 (2006) no. 4, pp. 275-278. doi : 10.1016/j.crma.2005.11.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.11.016/
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