On Asymptotic Expansions in the “Interval” CLT for Sums of Independent Random Vectors
We study the remainder term taking into account the asymptotic expansions in the multidimensional central limit theorem for sums of independent random vectors. The dependence of the remainder term on the measure of hitting set is studied.
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- 2.S. V. Fomin, “Asymptotic expansions in the multidimensional central limit theorem,” Vestn. Leningr. Univ., Mat. Mekh. Astr., 1, Vyp. 7, 116–118 (1982).Google Scholar
- 3.R. N. Bhattacharya and R. Ranga Rao, Normal Approximation and Asymptotic Expansions, John Wiley & Sons (1976).Google Scholar
- 4.A. Bikelis, “On the central limit theorem in Rk. I,” Litovsk. Mat. Sb., XI, 1, 27–58 (1971).Google Scholar
- 5.V. V. Petrov, Limit Theorems for Sums of Independent Random Variables [in Russian] Moscow (1972).Google Scholar
- 8.L. V. Rozovsky, “The convergence of the distribution functions of a sequence of sums of independent random variables to the normal law in Lp,” Litovsk. Mat. Sb., XVI, No. 1, 193–206 (1976).Google Scholar
- 10.L. V. Rozovsky, “The rate of convergence in the Lindeberg–Feller theorem,” Vestn. Leningr. Univ., Mat. Mekh. Astr., Vyp. 1, 70–75 (1974).Google Scholar