scholarly journals Tail Probabilities and Partial Moments for Quadratic Forms in Multivariate Generalized Hyperbolic Random Vectors

2013 ◽  
Author(s):  
Simon A. Broda
Keyword(s):  
Quadratic Forms ◽  
Tail Probabilities ◽  
Random Vectors

scholarly journals On quadratic forms in multivariate generalized hyperbolic random vectors

Biometrika ◽  
2020 ◽  
Author(s):  
Simon A Broda ◽  
Juan Arismendi Zambrano
Keyword(s):  
Least Squares ◽  
Quadratic Forms ◽  
Inversion Formula ◽  
Expected Shortfall ◽  
Distribution Functions ◽  
Least Squares Estimator ◽  
Tail Probabilities ◽  
Random Vectors ◽  
Two Stage ◽  
Approximate Expressions

Summary This article presents exact and approximate expressions for tail probabilities and partial moments of quadratic forms in multivariate generalized hyperbolic random vectors. The derivations involve a generalization of the classic inversion formula for distribution functions (Gil-Pelaez, 1951). Two numerical applications are considered: the distribution of the two-stage least squares estimator and the expected shortfall of a quadratic portfolio.

scholarly journals Stochastic Dominance and Weak Concentration for Sums of Independent Symmetric Random Vectors

2018 ◽  
Vol 2020 (23) ◽  
pp. 8997-9010
Author(s):  
Witold Bednorz ◽  
Tomasz Tkocz
Keyword(s):  
Stochastic Dominance ◽  
Tail Probabilities ◽  
Random Vectors ◽  
Weak Concentration

Abstract Kwapień and Woyczyński asked in their monograph (1992) whether their notion of superstrong domination is inherited when taking sums of independent symmetric random vectors (one vector dominates another if, essentially, tail probabilities of any norm of the two vectors compare up to some scaling constants). We answer this question positively. As a by-product of our methods, we establish that a certain notion of weak concentration is also preserved by taking sums of independent symmetric random vectors.

scholarly journals Tail probabilities for infinite series of regularly varying random vectors

Bernoulli ◽  
2008 ◽  
Vol 14 (3) ◽  
pp. 838-864 ◽  
Author(s):  
Henrik Hult ◽  
Gennady Samorodnitsky
Keyword(s):  
Infinite Series ◽  
Tail Probabilities ◽  
Random Vectors ◽  
Regularly Varying

Moments of skew-normal random vectors and their quadratic forms

2001 ◽  
Vol 51 (4) ◽  
pp. 319-325 ◽  
Author(s):  
Marc G. Genton ◽  
Li He ◽  
Xiangwei Liu
Keyword(s):  
Quadratic Forms ◽  
Random Vectors ◽  
Skew Normal
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