A Quantile Estimator with Parametric and Nonparametric Features

摘要

We propose a new estimator for the quantile function with both, parametric and nonparametric features. A flexible parametric start represented by the g-and-h quantile function is corrected in a nonparametric fashion for potential misspecification. The combined estimator enjoys the same variance properties as the pure nonparametric kernel quantile estimator, but leaves room for substantial bias reduction. The new estimator performs well for extreme quantiles, as demonstrated by Monte Carlo simulations, and should therefore be helpful in finance and insurance applications.