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.
Citation
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
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