Abstract:
In the paper, an estimate for the rate of convergence of sums of independent random vectors is obtained which is non-uniform and non-classical (i. e. it depends on the closeness of summand's distributions to the normal one). This estimate takes also into account the tail behaviour of summands' distributions.
Citation:
S. Ya. Šorgin, “A non-classical estimate of the rate of convergence in the multidimensional central limit theorem which takes into account large deviations”, Teor. Veroyatnost. i Primenen., 23:3 (1978), 692–697; Theory Probab. Appl., 23:3 (1979), 667–671
\Bibitem{Sho78}
\by S.~Ya.~{\v S}orgin
\paper A non-classical estimate of the rate of convergence in the multidimensional central limit theorem which takes into account large deviations
\jour Teor. Veroyatnost. i Primenen.
\yr 1978
\vol 23
\issue 3
\pages 692--697
\mathnet{http://mi.mathnet.ru/tvp3095}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=509749}
\zmath{https://zbmath.org/?q=an:0395.60027}
\transl
\jour Theory Probab. Appl.
\yr 1979
\vol 23
\issue 3
\pages 667--671
\crossref{https://doi.org/10.1137/1123082}
Linking options:
https://www.mathnet.ru/eng/tvp3095
https://www.mathnet.ru/eng/tvp/v23/i3/p692
This publication is cited in the following 4 articles:
Z. Rychlik, “Nonuniform central limit bounds with applications to probabilities of deviations”, Theory Probab. Appl., 28:4 (1984), 681–687
M. U. Gafurov, V. I. Rotar', “On the exit of random walk out of the curvilinear domain”, Theory Probab. Appl., 28:1 (1984), 179–184
V. I. Rotar', “On summation of independent variables in a non-classical situation”, Russian Math. Surveys, 37:6 (1982), 151–175
S. Ya. Šorgin, “Non-classical estimates of the rate of convergence in the central limit theorem which take into account large deviations”, Theory Probab. Appl., 27:2 (1983), 324–337