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

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

2007-02-12

arxiv.org/abs/math/0702326v2

Electronic Journal of Statistics 2008, Vol. 2, 516-541

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/07-EJS117 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/07-EJS117

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 \citeDebbarhViallon3. 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.

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