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Edgeworth Expansions for Multivariate Random Sums

Farrukh Javed (), Nicola Loperfido () and Stepan Mazur ()
Additional contact information
Farrukh Javed: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden, https://www.oru.se/english/employee/farrukh_javed
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden, https://www.oru.se/english/employee/stepan_mazur

No 2020:9, Working Papers from Örebro University, School of Business

Abstract: The sum of a random number of independent and identically distributed random vectors has a distribution which is not analytically tractable, in the general case. The problem has been addressed by means of asymptotic approximations embedding the number of summands in a stochastically increasing sequence. Another approach relies on tting exible and tractable parametric, multivariate distributions, as for example nite mixtures. In this paper we investigate both approaches within the framework of Edgeworth expansions. We derive a general formula for the fourth-order cumulants of the random sum of independent and identically distributed random vectors and show that the above mentioned asymptotic approach does not necessarily lead to valid asymptotic normal approximations. We address the problem by means of Edgeworth expansions. Both theoretical and empirical results suggest that mixtures of two multivariate normal distributions with proportional covariance matrices satisfactorily t data generated from random sums where the counting random variable and the random summands are Poisson and multivariate skew-normal, respectively.

Keywords: Edgeworth expansion; Fourth cumulant; Random sum; Skew-normal (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
Pages: 33 pages
Date: 2020-10-07
New Economics Papers: this item is included in nep-ecm and nep-ore
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