Statistics/Probability Theory
Asymptotic properties of the kernel estimator of the conditional mode for the left truncated model
Comptes Rendus. Mathématique, Volume 344 (2007) no. 10, pp. 651-656.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.03.023
Ould-Saïd, Elias 1; Tatachak, Abdelkader 2

1 L.M.P.A. J. Liouville, Université du littoral côte d'opale, BP 699, 62228 Calais, France
2 Laboratoire M.S.T.D, U.S.T.H.B, faculté de mathématiques, BP 32, El-Alia, 16111, Algeria
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Ould-Saïd, Elias; Tatachak, Abdelkader. Asymptotic properties of the kernel estimator of the conditional mode for the left truncated model. Comptes Rendus. Mathématique, Volume 344 (2007) no. 10, pp. 651-656. doi : 10.1016/j.crma.2007.03.023. http://www.numdam.org/articles/10.1016/j.crma.2007.03.023/

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