.svg){kind=logo}
ON THE CONVERGENCE OF RECURSIVE KERNEL DENSITY ESTIMATORS FOR WIDELY ORTHANT DEPENDENT AND CENSORED DATA
Keywords:
density, kernel estimator, widely orthant dependent, almost sure convergence.DOI:
https://doi.org/10.17654/0972086325002Abstract
In this article, we establish the almost sure convergence of a family of recursive estimators when the data are censored checking widely orthant dependence (WOD). The dependence hypothesis gives this work a certain originality because most often, the study of censored data is done with an independence hypothesis and in reality the real data are often dependent.
Received: August 14, 2024
Accepted: October 23, 2024
References
P. Deheuvels and J. Einmahl, Functional limit laws for the increments of Kaplan-Meier product limit processes and applications, Ann. Probab. 28 (2000), 1301-1335.
M. Duflo, Random iterative models, Collection Applications of Mathematics, Springer-Verlag, Berlin, Heidelberg, Vol. 34, 1997.
DOI: 10.1007/978-3-662-12880-0.
A. Jmaei, Y. Slaoui and W. Dellagi, Recursive distribution estimators defined by stochastic approximation method using Bernstein polynomials, J. Nonparametr. Stat. 29 (2017), 792-805. DOI 10.1080/10485252.2017.1369538.
E. L. Kaplan and P. Meier, Non parametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457-481.
H. Robbins and S. Monro, A stochastic approximation method, Ann. Math. Stat. 22(2) (1951), 400-407.
Y. Slaoui, Smoothing parameters for recursive kernel density estimators under censoring, Communications on Stochastic Analysis 13(2) (2019), Article 2.
B. Tsybakov, Recursive estimation of the mode of a multivariate distribution, Problems Inform. Transmission 26(1) (1990), 31-37.
Y. Li, Y. Zhou and C. Liu, On the convergence rates of kernel estimator and hazard estimator for widely dependent samples, J. Inequal. Appl. 2018 (2018), Article number 71. https://doi.org/10.1186/s13660-018-1659-1.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Far East Journal of Theoretical Statistics, PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pusha Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pusha Publishing House for more info or permissions.
