Short Communications

Some estimates of the accuracy of approximation in the multidimensional central limit theorem

I. S. Šiganov

Moscow

Abstract: The paper contains some estimates of the remainder term in the central limit theorem for the case of general Banach space and for its particular case $R_m$ ($m\le 5$). In the case of general Banach space the special metrics $\lambda_k$ are used, which are defined by means of characteristic functions. In the case of $R_m$ ($m\le 5$) we use the well-known Levy–Prohorov metrics.

Received: 12.03.1979

 English version: Theory of Probability and its Applications, 1980, 24:3, 626–629

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