Nonuniform bounds on the error of the normal approximation in \(H\) (Q1175854)

A new nonuniform estimate of remainder term in the so-called short asymptotic expansion in the central limit theorem in Hilbert space for nonidentically distributed summands is given. For previous results in i.i.d. case see \textit{V. Bentkus} and \textit{B. A. Zalesskii} [Lith. Math. J. 25, 199--208 (1985); translation from Litov. Mat. Sb. 25, No. 3, 3--16 (1985; Zbl 0585.60011)] and \textit{V. V. Sazonov}, \textit{V. V. Ul'yanov} and \textit{B. A. Zalesskii} [First World Congress of the Bernoulli Society of Math. Stat. and Probab. Theory, Abstr. Vol. 2, Moscow 1986, 782--783].