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Empirical likelihood inference for multiple censored samples
Author(s) -
Cai Song,
Chen Jiahua
Publication year - 2018
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11348
Subject(s) - quantile , estimator , censoring (clinical trials) , outlier , inference , mathematics , empirical likelihood , statistics , econometrics , nonparametric statistics , quantile function , statistical inference , asymptotic distribution , probability density function , computer science , cumulative distribution function , artificial intelligence
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. The Canadian Journal of Statistics 46: 212–232; 2018 © 2017 Statistical Society of Canada