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L-estimators and M-estimators for doubly censored data. (English) Zbl 0881.62054

Summary: Motivated by estimation and testing with doubly censored data, we study (robust) \(L\)-estimators and \(M\)-estimators based on such data. These estimators are given through functionals of the self-consistent estimator \(S^{(n)}_X\) for the survival function with doubly censored data. We show that a Hadamard differentiable functional of \(S^{(n)}_X\) is asymptotically normal. Thereby, the asymptotic normality of the proposed \(L\)-estimators and \(M\)-estimators for doubly censored data are derived via their Hadamard differentiability properties. The estimates for the asymptotic variances of the proposed estimators are also given and shown to be strongly consistent. The proposed estimators are applied to a doubly censored data set encountered in breast cancer research.

MSC:

62G20 Asymptotic properties of nonparametric inference
62G35 Nonparametric robustness
62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
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