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arXiv · 0901.4628

Functional asymptotic confidence intervals for a common mean of independent random variables

Yuliya V. Martsynyuk
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Abstract

We consider independent random variables (r.v.'s) with a common mean $μ$ that either satisfy Lindeberg's condition, or are symmetric around $μ$. Present forms of existing functional central limit theorems (FCLT's) for Studentized partial sums of such r.v.'s on $D[0,1]$ are seen to be of some use for constructing asymptotic confidence intervals, or what we call functional asymptotic confidence intervals (FACI's), for $μ$. In this paper we establish completely data-based versions of these FCLT's and thus extend their applicability in this regard. Two special examples of new FACI's for $μ$ are presented.

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Yuliya V. Martsynyuk. 2009-01-29. Functional asymptotic confidence intervals for a common mean of independent random variables. https://doi.org/10.1214/08-ejs233

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