DEFICIENCY OF THE SAMPLE QUANTILE ESTIMATOR WITH RESPECT TO KERNEL QUANTILE ESTIMATORS FOR CENSORED-DATA

Consider a statistical procedure (Method A) which is based on n observ ations and a less effective procedure (Method B) which requires a larg er number k(n) of observations to give equal performance under a certa in criterion. To compare two different procedures, Hedges and Lehmann suggested that the difference k(n) - n, called the deficiency of Metho d B with respect to Method A, is the most natural quantity to examine. In this article, the performance of two kernel quantile estimators is examined versus the sample quantile estimator under the criterion of equal covering probability for randomly right-censored data. We shall show that the deficiency of the sample quantile estimator with respect to the kernel quantile estimators is convergent to infinity with the maximum rate when the bandwidth is chosen to be optimal. A Monte Carlo study is performed, along with an illustration on a real data set.