Asymptotic properties of the kernel estimator of the conditional mode for the left truncated model

Elias Ould-Saïd; Abdelkader Tatachak

doi:10.1016/j.crma.2007.03.023

Statistics/Probability Theory

Asymptotic properties of the kernel estimator of the conditional mode for the left truncated model

Presented by: Paul Deheuvels

Elias Ould-Saïd ¹; Abdelkader Tatachak 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

Comptes Rendus. Mathématique, Volume 344 (2007) no. 10, pp. 651-656.

Abstract
Résumé

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: 2006-06-27
Accepted: 2007-03-23
Published online: 2007-05-07

DOI: 10.1016/j.crma.2007.03.023

Author's affiliations:

Elias Ould-Saïd ¹; Abdelkader Tatachak 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

@article{CRMATH_2007__344_10_651_0,
     author = {Elias Ould-Sa{\"\i}d and Abdelkader Tatachak},
     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},
}

TY  - JOUR
AU  - Elias Ould-Saïd
AU  - Abdelkader Tatachak
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
DO  - 10.1016/j.crma.2007.03.023
LA  - en
ID  - CRMATH_2007__344_10_651_0
ER  -

%0 Journal Article
%A Elias Ould-Saïd
%A Abdelkader Tatachak
%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
%R 10.1016/j.crma.2007.03.023
%G en
%F CRMATH_2007__344_10_651_0

Elias Ould-Saïd; Abdelkader Tatachak. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.03.023/

References
Cited by

[1] S. He; G.L. Yang Estimation of the truncation probability in the random truncation model, Ann. Statist., Volume 26 (1998), pp. 1011-1027

[2] D. Lynden-Bell 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] E. Ould-Saïd; M. Lemdani Asymptotic properties of a nonparametric regression function estimator with randomly truncated data, Ann. Inst. Statist. Math., Volume 58 (2006), pp. 357-378

[4] M. Samanta; A. Thavaneswaran Nonparametric estimation of the conditional mode, Comm. Statist. Theory Methods, Volume 19 (1990), pp. 4515-4524

[5] W. Stute Almost sure representations of the product-limit estimator for truncated data, Ann. Statist., Volume 21 (1993), pp. 146-156

[6] M. Woodroofe Estimating a distribution function with truncated data, Ann. Statist., Volume 13 (1985), pp. 163-177

Cited by Sources:

Comments - Policy