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September, 1978 Nonparametric Estimation for Nonhomogeneous Markov Processes in the Problem of Competing Risks
Thomas R. Fleming
Ann. Statist. 6(5): 1057-1070 (September, 1978). DOI: 10.1214/aos/1176344310

Abstract

Consider a time-continuous nonhomogeneous Markovian stochastic process $V$ having state space $A^0$. Let $A \subset A^0$ and let $P_{Aij}(\tau, t)$ be the $i \rightarrow j$ transition probability of the Markovian stochastic process $V_A$ arising in the hypothetical situation where states $A^0 - A$ have been eliminated from the state space of $V$. Based upon the concept of Kaplan and Meier's product-limit estimator, a nonparametric estimator $\hat{P}_{Aij}(\tau, t)$ is formulated which is proved to be uniformly strongly consistent and asymptotically unbiased. These results generalize those by Aalen for the special case in which $A^0$ has one transient state.

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Thomas R. Fleming. "Nonparametric Estimation for Nonhomogeneous Markov Processes in the Problem of Competing Risks." Ann. Statist. 6 (5) 1057 - 1070, September, 1978. https://doi.org/10.1214/aos/1176344310

Information

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

zbMATH: 0389.62033
MathSciNet: MR499572
Digital Object Identifier: 10.1214/aos/1176344310

Subjects:
Primary: 62G05
Secondary: 60J75 , 62N05

Keywords: competing risks , consistency , nonhomogeneous , nonparametric , Product limit

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 5 • September, 1978
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