Geodesic
On the rate of approximation in the random sum CLT for dependent variables
Applications of Mathematics, Tome 32 (1987) no. 3, pp. 169-176.

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Capital $"O"$ and lower-case $"o"$ approximations of the expected value of a class of smooth functions $(f\in C^r(R))$ of the normalized random partial sums of dependent random variables by the expectation of the corresponding functions of Gaussian random variables are established. The same types of approximation are also obtained for dependent random vectors. This generalizes and improves previous results of the author (1980) and Rychlik and Szynal (1979).
DOI : 10.21136/AM.1987.104248
Classification : 41A25, 60F05, 60G42
Keywords: random sums; central limit theorem; approximation theorems; random vectors 
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Basu, Adhir Kumar. On the rate of approximation in the random sum CLT for dependent variables. Applications of Mathematics, Tome 32 (1987) no. 3, pp. 169-176. doi : 10.21136/AM.1987.104248. http://geodesic.mathdoc.fr/articles/10.21136/AM.1987.104248/

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