Abstract
In this article, we summarize some quantile estimators and related bandwidth selection methods and give two new bandwidth selection methods. By four distributions: standard normal, exponential, double exponential and log normal we simulated the methods and compared their efficiencies to that of the empirical quantile. It turns out that kernel smoothed quantile estimators, with no matter which bandwidth selection method used, are more efficient than the empirical quantile estimator in most situations. And when sample size is relatively small, kernel smoothed estimators are especially more efficient than the empirical quantile estimator. However, no one method can beat any other methods for all distributions.
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