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Closed Likelihood Ratio Testing Procedures to Assess Similarity of Covariance Matrices

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  • Francesca Greselin
  • Antonio Punzo

Abstract

In this article, we introduce a multiple testing procedure to assess a common covariance structure between k groups. The new test allows for a choice among eight different patterns arising from the three-term eigen decomposition of the group covariances. It is based on the closed testing principle and adopts local likelihood ratio (LR) tests. The approach reveals richer information about the underlying data structure than classical methods, the most common one being only based on homo/heteroscedasticity. At the same time, it provides a more parsimonious parameterization, whenever the constrained model is suitable to describe the real data. The new inferential methodology is then applied to some well-known datasets chosen from the multivariate literature. Finally, simulation results are presented to investigate its performance in different situations representing gradual departures from homoscedasticity and to evaluate the reliability of using the asymptotic χ-super-2 to approximate the actual distribution of the local LR test statistics.

Suggested Citation

  • Francesca Greselin & Antonio Punzo, 2013. "Closed Likelihood Ratio Testing Procedures to Assess Similarity of Covariance Matrices," The American Statistician, Taylor & Francis Journals, vol. 67(3), pages 117-128, August.
  • Handle: RePEc:taf:amstat:v:67:y:2013:i:3:p:117-128
    DOI: 10.1080/00031305.2013.791643
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    Citations

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    Cited by:

    1. Luca Bagnato & Antonio Punzo, 2021. "Unconstrained representation of orthogonal matrices with application to common principal components," Computational Statistics, Springer, vol. 36(2), pages 1177-1195, June.
    2. Maruotti, Antonello & Punzo, Antonio, 2017. "Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 475-496.
    3. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 85-113, April.
    4. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    5. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "Erratum to: The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 327-355, July.
    6. Salvatore D. Tomarchio & Luca Bagnato & Antonio Punzo, 2022. "Model-based clustering via new parsimonious mixtures of heavy-tailed distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(2), pages 315-347, June.
    7. Dariush Najarzadeh & Mojtaba Khazaei & Mojtaba Ganjali, 2015. "Testing for equality of ordered eigenvectors of two multivariate normal populations," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 57-72, April.
    8. Dariush Najarzadeh, 2019. "Testing equality of standardized generalized variances of k multivariate normal populations with arbitrary dimensions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 593-623, December.
    9. Tortora, Cristina & Franczak, Brian C. & Bagnato, Luca & Punzo, Antonio, 2024. "A Laplace-based model with flexible tail behavior," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).

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