Optimal model selection for density estimation of stationary data under various mixing conditions

TL;DR

This paper introduces a block-resampling penalization technique for density estimation in stationary data with mixing conditions, providing theoretical guarantees and a data-driven method for penalty optimization.

Contribution

It develops a novel block-resampling penalization approach for density estimation under mixing conditions, with proven oracle inequalities and a slope heuristic for penalty tuning.

Findings

Estimator satisfies oracle inequalities with asymptotic leading constant 1

Slope heuristic effectively optimizes the penalty in mixing data scenarios

Method extends density estimation techniques to dependent data contexts

Abstract

We propose a block-resampling penalization method for marginal density estimation with nonnecessary independent observations. When the data are $\beta$ or $\tau$-mixing, the selected estimator satisfies oracle inequalities with leading constant asymptotically equal to 1. We also prove in this setting the slope heuristic, which is a data-driven method to optimize the leading constant in the penalty.