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An empirical goodness-of-fit test for multivariate distributions

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  • Michael McAssey

Abstract

An empirical test is presented as a tool for assessing whether a specified multivariate probability model is suitable to describe the underlying distribution of a set of observations. This test is based on the premise that, given any probability distribution, the Mahalanobis distances corresponding to data generated from that distribution will likewise follow a distinct distribution that can be estimated well by means of a large sample. We demonstrate the effectiveness of the test for detecting departures from several multivariate distributions. We then apply the test to a real multivariate data set to confirm that it is consistent with a multivariate beta model.

Suggested Citation

  • Michael McAssey, 2013. "An empirical goodness-of-fit test for multivariate distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(5), pages 1120-1131.
    • Handle: RePEc:taf:japsta:v:40:y:2013:i:5:p:1120-1131
    DOI: 10.1080/02664763.2013.780160
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    Cited by:

    1. Leovardo Mata Mata & José Antonio Núñez Mora & Ramona Serrano Bautista, 2021. "Multivariate Distribution in the Stock Markets of Brazil, Russia, India, and China," SAGE Open, , vol. 11(2), pages 21582440211, April.
    2. Torri, Gabriele & Giacometti, Rosella & Paterlini, Sandra, 2018. "Robust and sparse banking network estimation," European Journal of Operational Research, Elsevier, vol. 270(1), pages 51-65.
    3. Stergios B. Fotopoulos & Venkata K. Jandhyala & Alex Paparas, 2021. "Some Properties of the Multivariate Generalized Hyperbolic Laws," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 187-205, February.
    4. Beatriz Mota Aragón & José Antonio Núñez Mora, 2019. "Estimación de la distribución multivariada de los rendimientos de los tipos de cambio contra el dólar de las criptomonedas Bitcoin, Ripple y Ether," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 14(3), pages 447-457, Julio - S.
    5. Jairo Cugliari & Antoine Rolland, 2018. "Simulation of multicriteria data," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 21-37, June.
    6. Soukissian, Takvor H. & Karathanasi, Flora E., 2017. "On the selection of bivariate parametric models for wind data," Applied Energy, Elsevier, vol. 188(C), pages 280-304.
    7. Sirao Wang & Jiajuan Liang & Min Zhou & Huajun Ye, 2022. "Testing Multivariate Normality Based on F -Representative Points," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    8. Fidel Ernesto Castro Morales & Dimitris N. Politis & Jacek Leskow & Marina Silva Paez, 2022. "Student’s-t process with spatial deformation for spatio-temporal data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1099-1126, December.
    9. Audrius Kabašinskas & Leonidas Sakalauskas & Ingrida Vaičiulytė, 2021. "An Analytical EM Algorithm for Sub-Gaussian Vectors," Mathematics, MDPI, vol. 9(9), pages 1-20, April.
    10. José Antonio Núñez Mora & Leovardo Mata Mata, 2016. "Covariances matrix under the multivariate-Gh funtion to desing portfolios," Contaduría y Administración, Accounting and Management, vol. 61(3), pages 535-550, Julio-Sep.
    11. Manuel L. Esquível & Nadezhda P. Krasii, 2023. "On Structured Random Matrices Defined by Matrix Substitutions," Mathematics, MDPI, vol. 11(11), pages 1-29, May.

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