Asymptotics for sums of a function of normalized independent sums
Abstract
We derive a central limit theorem for sums of a function of independent sums of independent and identically distributed random variables. In particular we show that previously known result from Rempa and Weso (Statist. Probab. Lett. 74 (2005) 129--138), which can be obtained by applying the logarithm as the function, holds true under weaker assumptions.
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