Bandwidth selections for a class of smooth quantile estimators
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In this thesis, we summarized some quantile estimators and related bandwidth selection methods. Then we gave 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 empirical quantile. It turns out kernel smoothing quantile estimators, no matter which bandwidth selection method is used, are more efficient than empirical quantile estimators in most situations. And when sample size is relatively small, kernel smoothing estimators are especially more efficient than empirical quantile estimators. However, no one method can beat any other methods for all distributions.