Multivariate elliptical truncated moments

Juan C. Arismendi and Simon Broda

Journal of Multivariate Analysis, 2017, vol. 157, issue C, 29-44

Abstract: In this study, we derive analytic expressions for the elliptical truncated moment generating function (MGF), the zeroth-, first-, and second-order moments of quadratic forms of the multivariate normal, Student’s t, and generalized hyperbolic distributions. The resulting formulas were tested in a numerical application to calculate an analytic expression of the expected shortfall of quadratic portfolios with the benefit that moment based sensitivity measures can be derived from the analytic expression. The convergence rate of the analytic expression is fast–one iteration–for small closed integration domains, and slower for open integration domains when compared to the Monte Carlo integration method. The analytic formulas provide a theoretical framework for calculations in robust estimation, robust regression, outlier detection, design of experiments, and stochastic extensions of deterministic elliptical curves results.

Keywords: Elliptical functions; Elliptical truncation; Multivariate truncated moments; Parametric distributions; Quadratic forms; Tail moments (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X17301239
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Multivariate Elliptical Truncated Moments (2016)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:157:y:2017:i:c:p:29-44

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2017.02.011

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().