Electronic Journal of Statistics

Uniform limit laws of the logarithm for estimators of the additive regression function in the presence of right censored data

Mohammed Debbarh and Vivian Viallon

Full-text: Open access

Abstract

It has been recently shown that nonparametric estimators of the additive regression function could be obtained in the presence of right censoring by coupling the marginal integration method with initial kernel-type Inverse Probability of Censoring Weighted estimators of the multivariate regression function [10]. In this paper, we get the exact rate of strong uniform consistency for such estimators. Our uniform limit laws especially lead to the construction of asymptotic simultaneous 100% confidence bands for the true regression function.

Article information

Source
Electron. J. Statist., Volume 2 (2008), 516-541.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1214491854

Digital Object Identifier
doi:10.1214/07-EJS117

Mathematical Reviews number (MathSciNet)
MR2417392

Zentralblatt MATH identifier
1320.62089

Subjects
Primary: 62G08: Nonparametric regression 62N01: Censored data models

Keywords
nonparametric estimation additive regression function right censored data uniform laws of the logarithm

Citation

Debbarh, Mohammed; Viallon, Vivian. Uniform limit laws of the logarithm for estimators of the additive regression function in the presence of right censored data. Electron. J. Statist. 2 (2008), 516--541. doi:10.1214/07-EJS117. https://projecteuclid.org/euclid.ejs/1214491854


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