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Random truncation models and Markov processes. (English) Zbl 0717.62073
Given $n$ independent and identically distributed replications of the conditional distribution, given $Y<X$, of a pair of independent random variables $Y$ and $X$ with distribution functions $G$ and $F$, the authors discuss nonparametric estimation of $G$ and $F$. They show that the basic statistical model can be embedded in a Markov process model and derive properties of some estimators by using the modern techniques of statistical inference in counting processes [{\it O. Aalen}, Ann. Stat. 6, 701--726 (1978; Zbl 0389.62025), and {\it P. K. Andersen} and {\it O. Borgan}, Scand. J. Stat., Theory Appl. 12, 97--158 (1985; Zbl 0584.62176)]. They further show that the estimators suggested by them can be interpreted as maximum likelihood estimators and derive the asymptotic properties of the estimators following results of {\it O. Aalen} and {\it S. Johansen} [ibid. 5, 141--150 (1978; Zbl 0383.62058)].

MSC:
62M05Markov processes: estimation
62G05Nonparametric estimation
62G20Nonparametric asymptotic efficiency
60G55Point processes
60G44Martingales with continuous parameter
62N02Estimation (survival analysis)
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