2022
DOI: 10.48550/arxiv.2202.04717
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The Central Limit Theorem for Weakly Dependent Random Variables by the Moment Method

Abstract: In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study depends solely on the separability of mixed moments. Our investigation yields a new proof for the CLT for α-mixing random variables, but also non-α-mixing random variables fit within our framework, such as MA(∞) processes. In particular, our results can be applied to ARMA(p, q) pr… Show more

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“…the student network parameters θ S which we try to optimize and thus by applying the gradient operator we can conclude that ∇ θ S L RemixIT ≈ ∇ θ S L Supervised . One could make this theorem even more applicable to realworld settings where the student errors given different bootstrapped mixtures from the initial teacher estimate s * are weakly dependent [49] but we defer this derivation to future work.…”
Section: ) Error Analysis Under the Euclidean Normmentioning
confidence: 99%
“…the student network parameters θ S which we try to optimize and thus by applying the gradient operator we can conclude that ∇ θ S L RemixIT ≈ ∇ θ S L Supervised . One could make this theorem even more applicable to realworld settings where the student errors given different bootstrapped mixtures from the initial teacher estimate s * are weakly dependent [49] but we defer this derivation to future work.…”
Section: ) Error Analysis Under the Euclidean Normmentioning
confidence: 99%