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December, 1983 Nonparametric Inference for Rates with Censored Survival Data
Brian S. Yandell
Ann. Statist. 11(4): 1119-1135 (December, 1983). DOI: 10.1214/aos/1176346326


This paper concerns nonparametric inference for hazard rates with censored serial data. The focus is upon "delta sequence" estimators of the form $h_n(x) = \int K_b(x, y) dH_n(y)$ with $K_b$ integrating to 1 and concentrating mass near $x$ as $b \rightarrow 0. H_n$ is the Nelson-Aalen empirical cumulative hazard. Strong approximation and simultaneous confidence bands are derived for Rosenblatt-Parzen estimators, with $K_b(x, y) = w((x - y)/b)/b, b = o(n^{-1}),$ and $w(\cdot)$ a well-behaved density. This work generalizes global deviation and mean square deviation results of Bickel and Rosenblatt and others to censored survival data. Simulations with exponential survival and censoring indicate the effect of censoring on bias, variance, and maximal absolute deviation. Data from a survival experiment with serial sacrifice are analysed.


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Brian S. Yandell. "Nonparametric Inference for Rates with Censored Survival Data." Ann. Statist. 11 (4) 1119 - 1135, December, 1983.


Published: December, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0598.62050
MathSciNet: MR720258
Digital Object Identifier: 10.1214/aos/1176346326

Primary: 62G05
Secondary: 62G10, 62G15, 62P10

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 4 • December, 1983
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