Rates of Approximation in the Multidimensional Invariance Principle for Sums of I.i.d. Random Vectors with Finite Moments
نویسندگان
چکیده
The aim of this paper is to derive some consequences of the main result of Götze and Zaitsev [5] (see Theorem 2 below). We shall show that the i.i.d. case of this result implies the multidimensional version of a result of Sakhanenko [12]. We shall obtain bounds for the rate of strong Gaussian approximation of sums of i.i.d. R-valued random vectors ξj having finite moments E ‖ξj‖ , γ > 2. We consider the following well-known problem. One has to construct on a probability space a sequence of independent random vectors X1, . . . , Xn (with given distributions) and a corresponding sequence of independent Gaussian random vectors Y1, . . . , Yn so that the quantity
منابع مشابه
ESAIM Probability and Statistics April Vol MULTIDIMENSIONAL VERSION OF THE RESULTS OF KOML OS MAJOR AND TUSN ADY FOR VECTORS WITH FINITE EXPONENTIAL MOMENTS
A multidimensional version of the results of Koml os Ma jor and Tusn ady for the Gaussian approximation of the sequence of successive sums of independent random vectors with nite exponential moments is obtained Introduction The statement of the problem is well known It is required to construct on a probability space a sequence of independent random vectors X Xn with given distributions and a co...
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