The general regularisation scheme applied to conditional density estimation

TL;DR

This paper introduces a unified regularisation framework for conditional density estimation, deriving a new estimator with proven convergence rates and demonstrating superior performance over traditional methods.

Contribution

It extends a versatile regularisation scheme to conditional density estimation and implements a computationally efficient Landweber regularisation approach.

Findings

The new estimator achieves convergence rates with theoretical guarantees.

Numerical experiments show it outperforms Nadaraya-Watson in various scenarios.

The approach is applicable to time series models.

Abstract

The general regularisation scheme, a versatile approach for nonparametric estimation, has been successfully applied to regression, density ratio, and score estimation. In this paper, we introduce a unified framework encompassing these settings and extend it to conditional density estimation, deriving a new estimator with rigorously established convergence rates. We implement the Landweber regularisation, which is computationally more tractable than Tikhonov regularisation in this context. Numerical experiments demonstrate that our estimator matches or outperforms the Nadaraya-Watson estimator in various scenarios, including time series models.