ℒ1-deficiency of the sample quantile estimator with respect to a kernel quantile estimator

The performance of the sample quantile estimator versus a kernel quantile estimator under the criterion of mean integrated absolute error (MIAE) for randomly right-censored data is considered in this paper. We show that the so called ℒ1-deficiency of the sample quantile estimator with respect to the kernel quantile estimator is convergent to infinity. The optimal bandwidth in the sense of MIAE is obtained. Some simulation studies and one real data analysis are used to illustrate the results.