Geodesic
On estimation of the remainder in the central limit theorem for sums of functions of independent random variables and sums of the form $\Sigma f(t2^k)$
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 1, pp. 108-116

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The result of [2] is generalized to the case of sums of functions of independent identically distributed random variables. The dependence of the remainder on $x$ in the theorem of [1] concerning sums of the form $\Sigma f(t2^k)$ is also investigated. In proofs, limit theorems for differently distributed independent summands are used instead of the characteristic function method. 
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     author = {V. I. Ladohin and D. A. Moskvin},
     title = {On estimation of the remainder in the central limit theorem for sums of functions of independent random variables and sums of the form $\Sigma f(t2^k)$},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {108--116},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a7/}
}
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V. I. Ladohin; D. A. Moskvin. On estimation of the remainder in the central limit theorem for sums of functions of independent random variables and sums of the form $\Sigma f(t2^k)$. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 1, pp. 108-116. http://geodesic.mathdoc.fr/item/TVP_1971_16_1_a7/