New robust confidence intervals for the mean under dependence

The goal of this paper is to indicate a new method for constructing normal confidence intervals the mean, when data coming from stochastic structures with possibly long memory, especially dependence structure not known or even existence density function. More precisely we introduce random smoothing suggested by kernel estimators regression are constructed under sole condition that sequence ergodic and has finite second moments mild on sample variance. Applications presented linear processes reversible Markov chains memory. • Our estimator satisfies CLT functional bandwidths sequence. We propose mean unquantified dependence. rules choose necessary in applications intervals. No need estimate memory parameter case long-memory processes. This provides striking results as shown simulation section.