Dans cette Note nous proposons un estimateur non paramétrique de la fonction mode conditionnel, lorsque la variable d'intérêt est assujettie à une troncature aléatoire à gauche. Nous établissons dans un premier temps la convergence uniforme presque sûre de l'estimateur ainsi que sa vitesse, puis nous en donnons la normalité asymptotique.
In this Note we propose a non-parametric kernel estimator of the conditional mode function, when the variable of interest is subject to random left-truncation. We establish the rate of the strong uniform consistency of the estimate as well as its asymptotic normality.
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@article{CRMATH_2007__344_10_651_0, author = {Ould-Sa{\"\i}d, Elias and Tatachak, Abdelkader}, title = {Asymptotic properties of the kernel estimator of the conditional mode for the left truncated model}, journal = {Comptes Rendus. Math\'ematique}, pages = {651--656}, publisher = {Elsevier}, volume = {344}, number = {10}, year = {2007}, doi = {10.1016/j.crma.2007.03.023}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.03.023/} }
TY - JOUR AU - Ould-Saïd, Elias AU - Tatachak, Abdelkader TI - Asymptotic properties of the kernel estimator of the conditional mode for the left truncated model JO - Comptes Rendus. Mathématique PY - 2007 SP - 651 EP - 656 VL - 344 IS - 10 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.03.023/ DO - 10.1016/j.crma.2007.03.023 LA - en ID - CRMATH_2007__344_10_651_0 ER -
%0 Journal Article %A Ould-Saïd, Elias %A Tatachak, Abdelkader %T Asymptotic properties of the kernel estimator of the conditional mode for the left truncated model %J Comptes Rendus. Mathématique %D 2007 %P 651-656 %V 344 %N 10 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.03.023/ %R 10.1016/j.crma.2007.03.023 %G en %F CRMATH_2007__344_10_651_0
Ould-Saïd, Elias; Tatachak, Abdelkader. Asymptotic properties of the kernel estimator of the conditional mode for the left truncated model. Comptes Rendus. Mathématique, Tome 344 (2007) no. 10, pp. 651-656. doi : 10.1016/j.crma.2007.03.023. http://archive.numdam.org/articles/10.1016/j.crma.2007.03.023/
[1] Estimation of the truncation probability in the random truncation model, Ann. Statist., Volume 26 (1998), pp. 1011-1027
[2] A method of allowing for known observational selection in small samples applied to 3CR quasars, Monthly Notices Roy. Astronom. Soc., Volume 155 (1971), pp. 95-118
[3] Asymptotic properties of a nonparametric regression function estimator with randomly truncated data, Ann. Inst. Statist. Math., Volume 58 (2006), pp. 357-378
[4] Nonparametric estimation of the conditional mode, Comm. Statist. Theory Methods, Volume 19 (1990), pp. 4515-4524
[5] Almost sure representations of the product-limit estimator for truncated data, Ann. Statist., Volume 21 (1993), pp. 146-156
[6] Estimating a distribution function with truncated data, Ann. Statist., Volume 13 (1985), pp. 163-177
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