scholarly journals Asymptotic normality of quadratic forms with random vectors of increasing dimension

2018 ◽  
Vol 164 ◽  
pp. 22-39 ◽  
Author(s):  
Hanxiang Peng ◽  
Anton Schick
Keyword(s):  
Asymptotic Normality ◽  
Quadratic Forms ◽  
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.

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

Approximation of Quadratic Forms of Independent Random Vectors by Accompanying Laws

1998 ◽  
Vol 42 (2) ◽  
pp. 189-212 ◽  
Author(s):  
V. Bentkus ◽  
F. Götze ◽  
A. Yu. Zaitsev
Keyword(s):  
Quadratic Forms ◽  
Random Vectors
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