The Harmonic Estimation Of High Conditional Quantiles Of Heavy-Tailed Distributions

The estimation of high conditional quantiles is very important in many fields. To model the effects of covariates x at tails of the response distribution Y, quantile regression provides an efficacious and natural way. In the other hands, when it comes to estimation at very high or low tails, conventional quantile regression estimation is often unstable and suffers from high variability especially for heavy-tailed distributions because of data sparsity. Moreover, contam-inated data will make the situation worse. In this paper, we consider the estimation problem of high conditional quantiles.We develop a new estimation method by combining the conventional quantile regression and the harmonic extreme value theory. Numerical results of our method for simulated data and two real applications are given to demonstrate the merits of our method. The contents of our paper are organized as follow:Section 1, we introduce the related theory and models.Section 2, we introduce a harmonic estimation of high conditional quantiles and its asymp-totic properties.Section 3, we show our numerical simulation results to analyze the robustness.Section 4, we evaluate the proposed method by the NSV data and EU-SILC Data.Section 5, we provide all the conditions and technical proofs of the main results.