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arxiv: 1006.0462 · v2 · pith:VHGLYNVVnew · submitted 2010-06-02 · 🧮 math.PR

Asymptotics for sums of a function of normalized independent sums

classification 🧮 math.PR
keywords sumsfunctionindependentapplyingassumptionsasymptoticscentralderive
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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\la and Weso\lowski (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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