Singular extended skew-elliptical distributions

Dı́az-Garcı́a, José A.; González–Farías, Graciela

doi:10.1016/j.jkss.2008.04.004

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…In other words, the distribution resulting from applying the corresponding statistical operation on the normal random vector and then do the hidden truncation process yields precisely the same distribution obtained if we do the operation after the truncation process. The exact formulas and results appear in Díaz-García and González-Farías, 2008 , Domínguez-Molina et al, 2003 , González-Farías et al, 2004a .…”

Section: Preliminariesmentioning

confidence: 99%

“…Due to its utility for this work, we specify the precise result for the closure under linear transformations. Namely, if

is a natural number,

is an

matrix of rank

, and

is an

-dimensional vector, then

where If

is an arbitrary matrix, the formula (4) remains valid if

is replaced with a symmetric generalized inverse of

( Díaz-García and González-Farías, 2008 ).…”

Section: Preliminariesmentioning

confidence: 99%

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A flexible special case of the CSN for spatial modeling and prediction

Márquez-Urbina¹,

González–Farías²

2022

Spatial Statistics

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We introduce a parsimonious, flexible subclass of the closed-skew normal (CSN) distribution that produces valid stationary spatial models. We derive and prove some relevant properties for this subfamily; in particular, we show that it is identifiable, closed under marginalization and conditioning and that a null correlation implies independence. Based on the subclass, we propose a discrete spatial model and its continuous version. We discuss why these random fields constitute valid models, and additionally, we discuss least-squares estimators for the models under the subclass. We propose to perform predictions on the model using the profile predictive likelihood; we discuss how to construct prediction regions and intervals. To compare the model against its Gaussian counterpart and show that the numerical likelihood estimators are well-behaved, we present a simulation study. Finally, we use the model to study a heuristic COVID-19 mortality risk index; we evaluate the model’s performance through 10-fold cross-validation. The risk index model is compared with a baseline Gaussian model.

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Section: Preliminariesmentioning

confidence: 99%

“…Due to its utility for this work, we specify the precise result for the closure under linear transformations. Namely, if

is a natural number,

is an

matrix of rank

, and

is an

-dimensional vector, then

where If

is an arbitrary matrix, the formula (4) remains valid if

is replaced with a symmetric generalized inverse of

( Díaz-García and González-Farías, 2008 ).…”

Section: Preliminariesmentioning

confidence: 99%

A flexible special case of the CSN for spatial modeling and prediction

Márquez-Urbina¹,

González–Farías²

2022

Spatial Statistics

Self Cite

View full text Add to dashboard Cite

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Matrix‐variate risk measures under Wishart and gamma distributions

Arias‐Serna,

Caro‐Lopera,

Loubes

2024

J Corp Accounting Finance

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Matrix‐variate distribution theory has been instrumental across various disciplines for the past seven decades. However, a comprehensive examination of financial literature reveals a notable gap concerning the application of matrix‐variate extensions to Value‐at‐Risk (VaR). However, from a mathematical perspective, the core requirement for VaR lies in determining meaningful percentiles within the context of finance, necessitating the consideration of matrix c.d.f. This paper introduces the concept of “matrix‐variate VaR” for both Wishart and Gamma distributions. To achieve this, we leverage the theory of hypergeometric functions of matrix argument and integrate over positive definite matrices. Our proposed approach adeptly characterizes a company's exposure by into a comprehensive risk measure. This facilitates a readily computable estimation of the total incurred risk. Notably, this approach enables efficient computation of risk measures under Wishart, exponential, Erlang, gamma, and chi‐square distributions. The resulting risk measures are expressed in closed analytic forms, enhancing their practical utility for day‐to‐day risk management.

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Portfolio separation properties of the skew-elliptical distributions, with generalizations

Framstad

2011

Statistics & Probability Letters

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Singular extended skew-elliptical distributions

Cited by 4 publications

References 18 publications

A flexible special case of the CSN for spatial modeling and prediction

A flexible special case of the CSN for spatial modeling and prediction

Matrix‐variate risk measures under Wishart and gamma distributions

Portfolio separation properties of the skew-elliptical distributions, with generalizations

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