A family of dimension-wise scaled normal mixtures (DSNMs) is proposed to model the joint distribution of a d-variate random variable with real-valued components. Each member of the family generalizes the multivariate normal (MN) distribution in two directions. Firstly, the DSNM has a more general type of symmetry with respect to the elliptical symmetry of the MN distribution and, secondly, the univariate marginals have similar heavy-tailed normal scale mixture distributions with (possibly) different tailedness parameters. As a consequence of practical interest, the DSNM allows for a different excess kurtosis on each dimension. We examine a number of properties of DSNMs and we describe two members of the DSNM family obtained in the case of components of the mixing random vector being either uniform or shifted exponential. These are examples of mixing distributions that guarantee a closed-form expression for the joint density of the DSNM. For the two DSNMs analyzed in detail, we describe algorithms, based on the expectation-maximization (EM) principle, to estimate the parameters by maximum likelihood. We use real data from the financial and biometrical fields to appreciate the advantages of our DSNMs over other symmetric heavy-tailed distributions available in the literature.

Bagnato, L., Punzo, A., A new family of multivariate centrally symmetric distributions, Abstract de <<24th International Conference on Computational Statistics (COMPSTAT 2022)>>, (Bologna, Italy, 23-26 August 2022 ), Elsevier, Bologna, Italy 2022: 1-107 [http://hdl.handle.net/10807/214913]

A new family of multivariate centrally symmetric distributions

Bagnato, Luca
Primo
;
2022

Abstract

A family of dimension-wise scaled normal mixtures (DSNMs) is proposed to model the joint distribution of a d-variate random variable with real-valued components. Each member of the family generalizes the multivariate normal (MN) distribution in two directions. Firstly, the DSNM has a more general type of symmetry with respect to the elliptical symmetry of the MN distribution and, secondly, the univariate marginals have similar heavy-tailed normal scale mixture distributions with (possibly) different tailedness parameters. As a consequence of practical interest, the DSNM allows for a different excess kurtosis on each dimension. We examine a number of properties of DSNMs and we describe two members of the DSNM family obtained in the case of components of the mixing random vector being either uniform or shifted exponential. These are examples of mixing distributions that guarantee a closed-form expression for the joint density of the DSNM. For the two DSNMs analyzed in detail, we describe algorithms, based on the expectation-maximization (EM) principle, to estimate the parameters by maximum likelihood. We use real data from the financial and biometrical fields to appreciate the advantages of our DSNMs over other symmetric heavy-tailed distributions available in the literature.
Inglese
PROGRAMME AND ABSTRACTS - 24th International Conference on Computational Statistics (COMPSTAT 2022)
24th International Conference on Computational Statistics (COMPSTAT 2022)
Bologna, Italy
23-ago-2022
26-ago-2022
978-90-73592-40-7
Elsevier
Bagnato, L., Punzo, A., A new family of multivariate centrally symmetric distributions, Abstract de <<24th International Conference on Computational Statistics (COMPSTAT 2022)>>, (Bologna, Italy, 23-26 August 2022 ), Elsevier, Bologna, Italy 2022: 1-107 [http://hdl.handle.net/10807/214913]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/214913
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact