Weighted quantile estimators

TL;DR

This paper introduces a flexible scheme for creating weighted quantile estimators, enhancing their application in tail distribution estimation and mixture models, with potential benefits in time series analysis.

Contribution

It presents a generic method for developing weighted versions of various quantile estimators, broadening their applicability in statistical analysis.

Findings

Weighted quantile estimators improve tail distribution estimation.

The approach is applicable to mixture distributions.

Enhanced quantile estimation in time series contexts.

Abstract

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.