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September, 1978 Asymptotic Distribution Results in Competing Risks Estimation
Thomas R. Fleming
Ann. Statist. 6(5): 1071-1079 (September, 1978). DOI: 10.1214/aos/1176344311

Abstract

Consider a time-continuous nonhomogeneous Markovian process $V$ having state space $A^0$. For $A \subset A^0$ and $i, j \in A, P_{Aij}(\tau, t)$ is the $i \rightarrow j$ transition probability of the Markovian process $V_A$ which arises in the hypothetical situation where states $A^0 - A$ have been eliminated from the state space of $V$. Let $\hat{P}_{Aij}(\tau, t)$ be the generalized product-limit estimator of $P_{Aij}(\tau,t)$. It is shown that the vector consisting of components in $\{N^\frac{1}{2}(\hat{P}_{Aij}(\tau, t) - P_{Aij}(\tau, t)): i, j \in A; i \neq j\}$ converges weakly to a vector of dependent Gaussian processes. The structure of this limiting vector process is studied. Finally these results are applied to the estimation of certain biometric functions.

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Thomas R. Fleming. "Asymptotic Distribution Results in Competing Risks Estimation." Ann. Statist. 6 (5) 1071 - 1079, September, 1978. https://doi.org/10.1214/aos/1176344311

Information

Published: September, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0405.62071
MathSciNet: MR499573
Digital Object Identifier: 10.1214/aos/1176344311

Subjects:
Primary: 62E20
Secondary: 60J75 , 62N05

Keywords: competing risks , expected survival time , nonhomogeneous , nonparametric , product-limit , weak convergence

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 5 • September, 1978
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