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On the functional limits for sums of a function of partial sums

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  • Kosinski, Kamil M.

Abstract

We derive a functional central limit theorem (fclt) for normalised sums of a function of the partial sums of independent and identically distributed random variables. In particular, we show, using a technique presented in Huang and Zhang [Huang, W., Zhang, L.-X., 2007. A note on the invariance principle of the product of sums of random variables. Electron. Comm. Probab. 12, 51-56] that the result from Qi [Qi, Y., 2003. Limit distributions for products of sums. Statist. Probab. Lett. 62, 93-100], for normalised products of partial sums, can be generalised in this fashion to a fclt.

Suggested Citation

  • Kosinski, Kamil M., 2009. "On the functional limits for sums of a function of partial sums," Statistics & Probability Letters, Elsevier, vol. 79(13), pages 1522-1527, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:13:p:1522-1527
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    References listed on IDEAS

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    1. Lu, Xuewen & Qi, Yongcheng, 2004. "A note on asymptotic distribution of products of sums," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 407-413, July.
    2. Qi, Yongcheng, 2003. "Limit distributions for products of sums," Statistics & Probability Letters, Elsevier, vol. 62(1), pages 93-100, March.
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