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- W2035581628 abstract "This paper provides a generalization of the classical Berry-Esseen theorem in two dimensions. For i.i.d. random variables $eta_1, eta_2, cdots, eta_r, cdots$ and real numbers $a_1, a_2, cdots, a_r, cdots$ and $b_1, b_2, cdots, b_r, cdots$ with $E(eta_r) = 0, E(eta_r^2) = 1, |a_r| leqq 1$ and $|b_r| leqq 1$, let $A_n^2 = sum^n_{r=1} a_r^2, B_n^2 = sum^n_{r=1} b_r^2$ and $S_n = (sum^n_{r=1} a_r eta_r/A_n, sum^n_{r=1} b_r eta_r/B_n)$. The main result concerns the rate of convergence of the distribution function of $S_n$ to the corresponding normal distribution function without assuming the existence of third moments. As an application of this result a theorem of P. Erdos and A. C. Offord is generalized." @default.
- W2035581628 created "2016-06-24" @default.
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- W2035581628 date "1975-10-01" @default.
- W2035581628 modified "2023-09-30" @default.
- W2035581628 title "On the Rate of Convergence in the Central Limit Theorem in Two Dimensions and its Application" @default.
- W2035581628 doi "https://doi.org/10.1214/aop/1176996267" @default.
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