Asymptotics for sums of a function of normalized independent sums

K.M. Kosinski

doi:10.1016/j.spl.2008.09.013

Asymptotics for sums of a function of normalized independent sums

K.M. Kosinski

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	415-419
Journal	Statistics and Probability Letters
Volume	79
Issue number	4
DOIs	https://doi.org/10.1016/j.spl.2008.09.013
Publication status	Published - 2009

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title = "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 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.",

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T1 - Asymptotics for sums of a function of normalized independent sums

AU - Kosinski, K.M.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

U2 - 10.1016/j.spl.2008.09.013

DO - 10.1016/j.spl.2008.09.013

M3 - Article

SN - 0167-7152

VL - 79

SP - 415

EP - 419

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

Asymptotics for sums of a function of normalized independent sums

Abstract

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