On the asymptotic behavior of randomly weighted averages

Rasool Roozegar and A.R. Soltani

Statistics & Probability Letters, 2015, vol. 96, issue C, 269-272

Abstract: In this paper we assume that X1,X2,… is a sequence of independent continuous centered random variables with finite variances σ12,σ22,…. Then we present a central limit theorem for the randomly weighted averages Sn=R1X1+⋯+RnXn, where the random weights R1,…,Rn are the cuts of (0,1) by the order statistics of a random sample of size n−1 from a uniform distribution on (0,1). Indeed we prove that under certain assumptions on the variances, n+1Sn converges in distribution to the normal distribution with mean zero and variance 2c, c=limn→∞(1/n)∑i=1nσi2.

Keywords: Central limit theorem; Limiting distribution; Randomly weighted average; Characteristic function; Normal, Semicircle and Arcsine distributions (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2014.10.003

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