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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.
Original languageUnknown
Title of host publicationAIP Conference Proceedings
Pages420-423
Volume1557
DOIs
Publication statusPublished - 1 Jan 2013
EventInternational Conference on Mathematical Sciences and Statistics (ICMSS) -
Duration: 1 Jan 2013 → …

Conference

ConferenceInternational Conference on Mathematical Sciences and Statistics (ICMSS)
Period1/01/13 → …

Keywords

    Cite this

    @inproceedings{5d7f229d458941048ed9eb61bc025234,
    title = "The multi-sample block-scalar sphericity test under the complex multivariate Normal case",
    abstract = "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.",
    keywords = "near-exact distributions, sphericity test, mixtures, asymptotic distributions, multi-sample, block-scalar, complex",
    author = "Marques, {Filipe Jos{\'e} Gon{\cc}alves Pereira} and Coelho, {Carlos Manuel Agra}",
    note = "O tipo de publica{\cc}{\~a}o ({"}publication type{"}) deve estar errado! Parece tratar-se de artigo de {"}proceedings{"} de confer{\^e}ncia (http://scitation.aip.org/content/aip/proceeding/aipcp/1557), mas os autores quiseram manter o tipo. Scopus: n{\~a}o foi poss{\'i}vel confirmar. WoS: est{\'a} indexado e classificado como {"}proceedings paper{"}. Salima Rehemtula: O artigo em quest{\~a}o {\'e} um {"}proceedings paper{"} de acordo com a WoS e a Scopus. J{\'a} alterei a tipologia.",
    year = "2013",
    month = "1",
    day = "1",
    doi = "10.1063/1.4823948",
    language = "Unknown",
    isbn = "978-0-7354-1183-8",
    volume = "1557",
    pages = "420--423",
    booktitle = "AIP Conference Proceedings",

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    Marques, FJGP & Coelho, CMA 2013, The multi-sample block-scalar sphericity test under the complex multivariate Normal case. in 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.

    AIP Conference Proceedings. Vol. 1557 2013. p. 420-423.

    Research output: Chapter in Book/Report/Conference proceedingConference 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.

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    KW - mixtures

    KW - asymptotic distributions

    KW - multi-sample

    KW - block-scalar

    KW - complex

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    DO - 10.1063/1.4823948

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    EP - 423

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