Kernel quantile estimator with ICI adaptive bandwidth selection technique

In this article, we consider a class of kernel quantile estimators which is the linear combination of order statistics. This class of kernel quantile estimators can be regarded as an extension of some existing estimators. The exact mean square error expression for this class of estimators will be provided when data are uniformly distributed. The implementation of these estimators depends mostly on the bandwidth selection. We then develop an adaptive method for bandwidth selection based on the intersection confidence intervals (ICI) principle. Monte Carlo studies demonstrate that our proposed approach is comparatively remarkable. We illustrate our method with a real data set.