An efficient algorithm for T-estimation

TL;DR

This paper presents a new efficient algorithm for T-estimation, including an exact and a faster approximate version, with applications in density estimation and model selection, demonstrated through empirical studies.

Contribution

It introduces a novel sub-quadratic complexity algorithm for T-estimation and provides an implementation in an R package for practical density estimation tasks.

Findings

The exact algorithm performs efficiently on large datasets.

The approximate version offers faster computation with minimal accuracy loss.

Empirical results show competitive performance in density estimation and model selection.

Abstract

We introduce an efficient and exact algorithm, together with a faster but approximate version, which implements with a sub-quadratic complexity the hold-out derived from T-estimation. We study empirically the performance of this hold-out in the context of density estimation considering well-known competitors (hold-out derived from least-squares or Kullback-Leibler divergence, model selection procedures, etc.) and classical problems including histogram or bandwidth selection. Our algorithms are integrated in a companion R-package called {\it Density.T.HoldOut} available on the CRAN: {\url{http://cran.r-project.org/web/packages/Density.T.HoldOut/index.html}}.