A law of the iterated logarithm for the empirical process based upon twice censored data. (English) Zbl 07819613
Malyarenko, Anatoliy (ed.) et al., Stochastic processes, statistical methods, and engineering mathematics. SPAS 2019, Västerås, Sweden, September 30 – October 2, 2019. Cham: Springer. Springer Proc. Math. Stat. 408, 163-177 (2022).
Summary: We give a functional law of the iterated logarithm for the increment functions of empirical processes with twice censored data. In this setting, the lifetime of interest \(X\) is right censored by a variable \(R\) and \(\min (X, R)\) is itself left censored by a variable \(L\). This model is however characterized by the independence of the latent variables \(X\), \(R\) and \(L\). We also derive strong laws for kernel estimators of the density and the failure rate of the lifetime \(X\). Our result extends the results available for complete or singly censored data.
For the entire collection see [Zbl 1515.60023].
For the entire collection see [Zbl 1515.60023].
MSC:
| 62N01 | Censored data models |
References:
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