A Note on Symmetric Bernoulli Random Variables
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This article is published in Annals of Mathematical Statistics.The article was published on 1970-08-01 and is currently open access. It has received 71 citations till now. The article focuses on the topics: Bernoulli process & Bernoulli trial.read more
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On Hoeffding’s inequalities
TL;DR: In this paper, a new type of inequality for tail probabilities of sums M n = X 1 +... + X n of bounded independent random variables X j was introduced, where the survival function x → P{S n ≥ x} has a jump down.
Journal ArticleDOI
Extremal Probabilistic Problems and Hotelling's $T^2$ Test Under a Symmetry Condition
TL;DR: In this paper, the authors considered the Hotelling $T^2$ statistic for an arbitrary $d$-dimensional sample and showed that if the sampling is not too deterministic or inhomogeneous, then under the zero-means hypothesis the limiting distribution for $T$ is Θ(chi^2_d).
Posted Content
Portfolio Diversification and Value At Risk Under Thick-Tailedness
TL;DR: In this article, the authors present a unified approach to value at risk analysis under heavy-tailedness using new majorization theory for linear combinations of thick-tailed random variables that they developed.
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Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities
TL;DR: The best constant and the extreme cases in an inequality of H.P. Rosenthal, relating the p moment of a sum of independent symmetric random variables to that of the p and 2 moments of the individual variables, are computed in the range 2 < p ≤ 4 as mentioned in this paper.
Book ChapterDOI
Optimal Tail Comparison Based on Comparison of Moments
TL;DR: In this paper, a moment comparison inequality is defined for a set of real functions on a measurable space (K, ∑) and a function ψ on K, where the objective is to find all the real functions satisfying (1) of the inequality.
References
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Book ChapterDOI
Probability Inequalities for sums of Bounded Random Variables
TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.
ReportDOI
Student's t-test under non-normal conditions
TL;DR: In this article, it was shown that assuming only a symmetry condition for the null hypothesis leads to effective bounds on the dispersion of the t-statistics of Student's t-test.