Inference concerning quantile for left truncated and right censored data

The problem of both testing and estimating the quantile function when the data are left truncated and right censored (LTRC) is considered. The aim of this communication is two-fold. First, a large sample test statistic to test for the quantile function under the LTRC model is defined and its null and non-null distributions are derived. A Monte Carlo simulation study is conducted to assess the power of the proposed test statistic that is used to define the estimators. Secondly, an improved estimation of the quantile function is investigated. In the spirit of the shrinkage principle in parameter estimation, three estimators assuming an uncertain prior non-sample information on the value of the quantile are proposed. The asymptotic bias and mean square error of the estimators are derived and compared with the usual estimator. The method is illustrated with hypothetical data as well as real data.

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