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A note on optimal probability lower bounds for centered random variables

Mark Veraar (2008)

Colloquium Mathematicae

We obtain lower bounds for ℙ(ξ ≥ 0) and ℙ(ξ > 0) under assumptions on the moments of a centered random variable ξ. The estimates obtained are shown to be optimal and improve results from the literature. They are then applied to obtain probability lower bounds for second order Rademacher chaos.

A note on stochastic ordering of estimators of exponential reliability

Piotr Nowak (2011)

Applicationes Mathematicae

Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which the maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered there and we prove that the MLEs for those plans are also stochastically ordered. We also give some applications to the estimation of reliability.

A note on the Ehrhard inequality

Rafał Latała (1996)

Studia Mathematica

We prove that for λ ∈ [0,1] and A, B two Borel sets in n with A convex, Φ - 1 ( γ n ( λ A + ( 1 - λ ) B ) ) λ Φ - 1 ( γ n ( A ) ) + ( 1 - λ ) Φ - 1 ( γ n ( B ) ) , where γ n is the canonical gaussian measure in n and Φ - 1 is the inverse of the gaussian distribution function.

A Note on the Men'shov-Rademacher Inequality

Witold Bednorz (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

We improve the constants in the Men’shov-Rademacher inequality by showing that for n ≥ 64, E ( s u p 1 k n | i = 1 k X i | ² 0 . 11 ( 6 . 20 + l o g n ) ² for all orthogonal random variables X₁,..., Xₙ such that k = 1 n E | X k | ² = 1 .

A second-order stochastic dominance portfolio efficiency measure

Miloš Kopa, Petr Chovanec (2008)

Kybernetika

In this paper, we introduce a new linear programming second-order stochastic dominance (SSD) portfolio efficiency test for portfolios with scenario approach for distribution of outcomes and a new SSD portfolio inefficiency measure. The test utilizes the relationship between CVaR and dual second-order stochastic dominance, and contrary to tests in Post [Post] and Kuosmanen [Kuosmanen], our test detects a dominating portfolio which is SSD efficient. We derive also a necessary condition for SSD efficiency...

A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions

Adam Osękowski (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Let X be a submartingale starting from 0, and Y be a semimartingale which is orthogonal and strongly differentially subordinate to X. The paper contains the proof of the sharp estimate ( s u p t 0 | Y t | 1 ) 3 . 375 . . . X . As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.

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