New robust confidence intervals for the mean under dependence

TL;DR

This paper introduces a new method for constructing robust confidence intervals for the mean in dependent data scenarios, especially with long memory and unknown dependence structures, using a novel random smoothing approach.

Contribution

It proposes a novel random smoothing technique based on kernel estimators to create confidence intervals under complex dependence structures.

Findings

Effective for linear processes with long memory

Applicable to reversible Markov chains

Provides reliable confidence intervals without density assumptions

Abstract

The goal of this paper is to indicate a new method for constructing normal confidence intervals for the mean, when the data is coming from stochastic structures with possibly long memory, especially when the dependence structure is not known or even the existence of the density function. More precisely we introduce a random smoothing suggested by the kernel estimators for the regression function. Applications are presented to linear processes and reversible Markov chains with long memory.