Quantile estimators and covering probabilities

Abstract

Based on an Edgeworth expansion for two kernel quantile estimators, the performance of the kernel quantile estimators is examined versus sample quantile estimator under the criterion of equal covering probability. The asymptotically optimal bandwidths is obtained corresponding to the maximum rate of convergence of the deficiency of the sample quantile estimator with respect to the kernel quantile estimators. A data-based procedure for optimal bandwidth selection is also investigated.

Keywords:

• Deficiency
• kernel estimator
• sample quantile
• covering probability
• Edgeworth expansion