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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 [O. Aalen, Ann. Stat. 6, 701–726 (1978; Zbl 0389.62025), and P. K. Andersen and 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 O. Aalen and S. Johansen [ibid. 5, 141–150 (1978; Zbl 0383.62058)].

MSC:
62M05 Markov processes: estimation; hidden Markov models
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G44 Martingales with continuous parameter
62N02 Estimation in survival analysis and censored data
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