A quantile-copula approach to conditional density estimation

TL;DR

This paper introduces a novel non-parametric kernel-based method for estimating conditional densities using quantile transforms and copula representation, offering a new approach with favorable theoretical properties.

Contribution

It proposes a new conditional density estimator leveraging quantile transforms and copulas, with analysis of its asymptotic behavior and comparison to existing methods.

Findings

The estimator has a remarkable product form due to copula representation.

Asymptotic properties of the estimator are established.

Compared bias and variance with nonparametric regression methods.

Abstract

We present a new non-parametric estimator of the conditional density of the kernel type. It is based on an efficient transformation of the data by quantile transform. By use of the copula representation, it turns out to have a remarkable product form. We study its asymptotic properties and compare its bias and variance to competitors based on nonparametric regression.