State occupation probabilities in non-Markov models. (English) Zbl 1442.62216
Let \(U=U(t)\), \(t\in[0,\infty)\) be a cadlag process with the state space \(\{1,\ldots, d\}\). Let \(\overrightarrow{p}(t)=(p_1(t), \ldots, p_d(t)\) be the vector of the state occupation probabilities \(p_i(t)=\mathbb{P}(U(t)=i)\) and \(P(s,t)=\{P_{ik}(s,t)\}\) be a transition \(d\times d\) matrix with conditional probabilities \(P_{ik}(s,t)=\mathbb{P}(U(t)=k\,|\,U(s)=i)\).
The author of the paper establishes the consistency of the Aalen-Johansen estimator [O. O. Aalen and S. Johansen, Scand. J. Stat., Theory Appl. 5, No. 3, 141–150 (1978; Zbl 0383.62058)] for the state occupation probabilities by using a new method. This new method is based on a simple identity for the state probabilities and on properties of additive and multiplicative transforms of the special interval functions.
The author of the paper establishes the consistency of the Aalen-Johansen estimator [O. O. Aalen and S. Johansen, Scand. J. Stat., Theory Appl. 5, No. 3, 141–150 (1978; Zbl 0383.62058)] for the state occupation probabilities by using a new method. This new method is based on a simple identity for the state probabilities and on properties of additive and multiplicative transforms of the special interval functions.
Reviewer: Jonas Šiaulys (Vilnius)
MSC:
| 62N02 | Estimation in survival analysis and censored data |
| 62N05 | Reliability and life testing |
| 62F12 | Asymptotic properties of parametric estimators |
| 62F40 | Bootstrap, jackknife and other resampling methods |
Keywords:
Aalen-Johansen estimator; interval function; additive transform; multiplicative transform; product integralCitations:
Zbl 0383.62058References:
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