On the Wasserstein distance for a martingale central limit theorem

On the Wasserstein distance for a martingale central limit theorem

We prove an upper bound on the Wasserstein distance between normalized martingales and the standard normal random variable, which extends a result of Röllin (2018). The proof is based on a method of Bolthausen (1982).

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Veröffentlicht in:Statistics & probability letters 2020-12, Vol.167, p.108892, Article 108892
Hauptverfasser: Fan, Xiequan, Ma, Xiaohui
Format: Artikel
Sprache:eng
Schlagworte:
Central limit theorem
Martingales
Wasserstein metric
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Zusammenfassung:We prove an upper bound on the Wasserstein distance between normalized martingales and the standard normal random variable, which extends a result of Röllin (2018). The proof is based on a method of Bolthausen (1982).
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2020.108892