Abstract:
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In the random censoring with completely unknown underlying distributions, the Nelson-Aalen and Kaplan-Meier estimators are known to be efficient as a functional of empirical distribution functions. They now have their quantile regression versions, originally suggested by Portnoy (2003, JASA). In this study, we investigate the efficiency gain in this context. Namely, since the regression quantiles reflect merely the empirical distribution, here we apply some efficient estimator for its coefficient functions at lower quantile, then construct a sequence of estimators which are regular and efficient conditionally on lower quantiles. This marginal efficiency will be carried over through Hadamard differentiable maps.
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