Uniformly root-$N$ consistent density estimators for weakly dependent invertible linear processes

TL;DR

This paper introduces a new kernel density estimator for stationary invertible linear processes that achieves a parametric convergence rate of n^{-1/2} in the supremum norm, improving upon traditional methods.

Contribution

The paper develops a novel residual-based kernel density estimator with optimal convergence rates for weakly dependent invertible linear processes.

Findings

Achieves uniform convergence at the parametric rate n^{-1/2}.

Provides new convergence rate results for residual-based kernel estimators.

Offers theoretical insights of independent interest for density estimation in dependent data.

Abstract

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate $n^{-1/2}$. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimators; these results are of independent interest.