Weighted quantile estimators

In this paper, we consider a generic scheme that allows building weighted versions of various quantile estimators, such as traditional quantile estimators based on linear interpolation of two order statistics, the Harrell-Davis quantile estimator and its trimmed modification. The obtained weighted quantile estimators are especially useful in the problem of estimating a distribution at the tail of a time series using quantile exponential smoothing. The presented approach can also be applied to other problems, such as quantile estimation of weighted mixture distributions.