Asymptotics for sums of a function of normalized independent sums

Kamil Kosinski

Statistics & Probability Letters, 2009, vol. 79, issue 4, 415-419

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 Rempala and Wesolowski [Rempala, G., Wesolowski, J., 2005. Asymptotics for products of independent sums with an application to Wishart determinants. Statist. Probab. Lett. 74 129-138], which can be obtained by applying the logarithm as the function, holds true under weaker assumptions.

Date: 2009
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