On the LIL for Self-Normalized Sums of IID Random Variables

Evarist Giné and David M. Mason

Journal of Theoretical Probability, 1998, vol. 11, issue 2, 351-370

Abstract: Abstract Let $$X,X_i ,i \in \mathbb{N},$$ be i.i.d. random variables and let, for each $$n \in \mathbb{N},S_n = \sum\nolimits_{i = 1}^n {X_i }$$ and $$V_n^2 = \sum\nolimits_{i = 1}^n {X_i^2 }$$ . It is shown that $$\lim \sup _{n \to \infty } {{|S_n |} \mathord{\left/ {\vphantom {{|S_n |} {(V_n \sqrt {\log \log n} )

Keywords: Self-normalized sums; law of the iterated logarithm; Feller class; Student t-statistic (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/A:1022675620729

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