Asymptotic constants for minimal distance in the central limit theorem. (English) Zbl 1225.60047

Rio, Emmanuel

Electron. Commun. Probab. 16, 96-103 (2011).

Summary: We generalize the asymptotic result of C.-G. Esseen [Tekn. Högskol. Handl. 121, 30 p. (1958; Zbl 0081.35202)] concerning the Wasserstein distance of order one in the mean central limit theorem to the Wasserstein distances of order \(r\) for \(r\in ]1,2]\)

MSC:

60F05

Central limit and other weak theorems

Keywords:

minimal metric; Wasserstein distance; Cornish-Fisher expansion; Esseen’s mean central limit theorem

Citations:

Zbl 0081.35202