# Empirical likelihood inference for multiple censored samples

## News

• Author: Song Cai and Jiahua Chen
• Date: 16 January 2019

In a paper published in The Canadian Journal of Statistics, the authors 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. Professors Cai and 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 paper is available via the link below and the authors explain their findings in further detail below:

Empirical likelihood inference for multiple censored samples

Song Cai and Jiahua Chen

The Canadian Journal of Statistics, Volume 46, Issue 2, June 2018, pages 212-232

Censored data are frequently encountered in scientific studies. Right-censored data with fixed censoring points, commonly known as Type I censored data, often arise from reliability engineering and medical studies, while left-censored data are frequently seen in environmental studies. For example, in programs for monitoring the concentrations of heavy metal, pesticides, or harmful chemicals in soil, when the actual concentration of a variable is below the lower detection limit of the measuring instrument, the data are left-censored at the detection limit.

In this paper, the authors develop a theory of semiparametric inference for multiple left-censored and/or right-censored random samples with fixed censoring points and explore methods to estimate their population quantiles and distribution functions. To efficiently use the information contained in multiple censored samples without imposing restrictive model assumptions, the authors use a semiparametric density ratio model (DRM) to feature pooled data across samples and propose an empirical likelihood (EL) approach to inference. Under this EL-DRM framework, the authors further propose population distribution function and quantile estimators with desirable mathematical properties.

These estimators are shown, both theoretically and numerically, to be more efficient than the classic nonparametric estimators such as the empirical distribution and sample quantile. Simulation studies suggest that the proposed methods are robust against misspecification of the density ratio function and against outliers. The proposed methods are illustrated with an application to the analysis of censored lumber strength data. These methods can be readily implemented with the R software package "drmdel".

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