Uniform Rates for Kernel Estimators of Weakly Dependent Data

TL;DR

This paper establishes new uniform convergence rates for kernel estimators applied to weakly dependent time series data, facilitating advanced asymptotic analysis in semiparametric models and risk measure estimation.

Contribution

It introduces uniform rate results for kernel estimators on dependent data, extending their applicability to infinite-dimensional classes and time series models.

Findings

Uniform convergence rates for kernel estimators under dependence.

Application to nonparametric estimation of Expected Shortfall.

Enhanced asymptotic theory for semiparametric time series models.

Abstract

This paper provides new uniform rate results for kernel estimators of absolutely regular stationary processes that are uniform in the bandwidth and in infinite-dimensional classes of dependent variables and regressors. Our results are useful for establishing asymptotic theory for two-step semiparametric estimators in time series models. We apply our results to obtain nonparametric estimates and their rates for Expected Shortfall processes.