We present a semiparametric approach to inference on the underlying distributions of multiple right- and/or left-censored samples with fixed censoring points and focus on effective estimation of population quantiles and distribution functions. We pool information across multiple censored samples through a semiparametric density ratio model and propose an empirical likelihood approach to inference. This approach achieves high efficiency without making restrictive model assumptions. The resultant estimator is asymptotically normal, and the resulting distribution function estimator and quantile estimator are more efficient than estimators obtained from the classic nonparametric methods, such as the empirical distribution and sample quantile. In addition, the proposed approach permits consistent estimation of distribution functions and quantiles on a larger domain than would otherwise be possible using the classic methods. Simulation studies suggest that the proposed method is robust against misspecification of the density ratio function and against outliers. Our approach is further illustrated with an application to the analysis of real lumber strength data.

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Keywords Asymptotic efficiency, Bahadur representation, CDF estimation, Dual partial empirical likelihood, Partial empirical likelihood, Quantile estimation
Persistent URL dx.doi.org/10.1002/cjs.11348
Journal Canadian Journal of Statistics
Citation
Cai, S, & Chen, J. (Jiahua). (2017). Empirical likelihood inference for multiple censored samples. Canadian Journal of Statistics. doi:10.1002/cjs.11348