### Abstract

Original language | Unknown |
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Title of host publication | AIP Conference Proceedings |

Pages | 420-423 |

Volume | 1557 |

DOIs | |

Publication status | Published - 1 Jan 2013 |

Event | International Conference on Mathematical Sciences and Statistics (ICMSS) - Duration: 1 Jan 2013 → … |

### Conference

Conference | International Conference on Mathematical Sciences and Statistics (ICMSS) |
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Period | 1/01/13 → … |

### Keywords

### Cite this

*AIP Conference Proceedings*(Vol. 1557, pp. 420-423) https://doi.org/10.1063/1.4823948

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*AIP Conference Proceedings.*vol. 1557, pp. 420-423, International Conference on Mathematical Sciences and Statistics (ICMSS), 1/01/13. https://doi.org/10.1063/1.4823948

**The multi-sample block-scalar sphericity test under the complex multivariate Normal case.** / Marques, Filipe José Gonçalves Pereira; Coelho, Carlos Manuel Agra.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - The multi-sample block-scalar sphericity test under the complex multivariate Normal case

AU - Marques, Filipe José Gonçalves Pereira

AU - Coelho, Carlos Manuel Agra

N1 - O tipo de publicação ("publication type") deve estar errado! Parece tratar-se de artigo de "proceedings" de conferência (http://scitation.aip.org/content/aip/proceeding/aipcp/1557), mas os autores quiseram manter o tipo. Scopus: não foi possível confirmar. WoS: está indexado e classificado como "proceedings paper". Salima Rehemtula: O artigo em questão é um "proceedings paper" de acordo com a WoS e a Scopus. Já alterei a tipologia.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - The multi-sample block-scalar sphericity test represents a wide family of tests since it has as particular cases several well known and fundamental tests in multivariate statistics, like for example the test of independence of several groups of variables, the sphericity test and the test of equality of several variance-covariance matrices. In this work we address the case where we have several independent samples extracted from complex multivariate Normal populations and we want to test if the covariance matrices are equal for all populations and if for each population they have a particular diagonal structure. We show that by decomposing the null hypothesis into three partial null hypotheses it is possible to easily derive the likelihood ratio test statistic, the expression of itsh-th moment and thecharacteristicfunction of its logarithm. Using this method we are able to betteranalyzethe structure of the exact distribution and, using the induced factorization on thecharacteristicfunction, we show how it is possible to develop simple but highly accurate near-exact distributions for the likelihood ratio test statistic.

AB - The multi-sample block-scalar sphericity test represents a wide family of tests since it has as particular cases several well known and fundamental tests in multivariate statistics, like for example the test of independence of several groups of variables, the sphericity test and the test of equality of several variance-covariance matrices. In this work we address the case where we have several independent samples extracted from complex multivariate Normal populations and we want to test if the covariance matrices are equal for all populations and if for each population they have a particular diagonal structure. We show that by decomposing the null hypothesis into three partial null hypotheses it is possible to easily derive the likelihood ratio test statistic, the expression of itsh-th moment and thecharacteristicfunction of its logarithm. Using this method we are able to betteranalyzethe structure of the exact distribution and, using the induced factorization on thecharacteristicfunction, we show how it is possible to develop simple but highly accurate near-exact distributions for the likelihood ratio test statistic.

KW - near-exact distributions

KW - sphericity test

KW - mixtures

KW - asymptotic distributions

KW - multi-sample

KW - block-scalar

KW - complex

U2 - 10.1063/1.4823948

DO - 10.1063/1.4823948

M3 - Conference contribution

SN - 978-0-7354-1183-8

VL - 1557

SP - 420

EP - 423

BT - AIP Conference Proceedings

ER -