IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/ws024211.html
   My bibliography  Save this paper

Singular random matrix decompositions: distributions

Author

Listed:
  • Díaz García, José A.
  • González Farías, Graciela

Abstract

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution.

Suggested Citation

  • Díaz García, José A. & González Farías, Graciela, 2002. "Singular random matrix decompositions: distributions," DES - Working Papers. Statistics and Econometrics. WS ws024211, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:ws024211
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/185/ws024211.pdf?sequence=1
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Díaz-García, José A. & Jáimez, Ramón Gutierrez & Mardia, Kanti V., 1997. "Wishart and Pseudo-Wishart Distributions and Some Applications to Shape Theory," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 73-87, October.
    2. Goodall, Colin & Mardia, Kanti V., 1992. "The noncentral Bartlett decompositions and shape densities," Journal of Multivariate Analysis, Elsevier, vol. 40(1), pages 94-108, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Díaz-García, José A. & González-Farías, Graciela, 2005. "Singular random matrix decompositions: distributions," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 109-122, May.
    2. Omer L. Gebizlioglu & Serap Yörübulut, 2016. "A Pseudo-Pareto Distribution and Concomitants of Its Order Statistics," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1043-1064, December.
    3. Kjetil B. Halvorsen & Victor Ayala & Eduardo Fierro, 2016. "On the Marginal Distribution of the Diagonal Blocks in a Blocked Wishart Random Matrix," International Journal of Analysis, Hindawi, vol. 2016, pages 1-5, November.
    4. José Díaz-García & Francisco Caro-Lopera, 2012. "Generalised shape theory via SV decomposition I," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(4), pages 541-565, May.
    5. Díaz-García, José A. & Gutiérrez-Jáimez, Ramón, 2006. "The distribution of the residual from a general elliptical multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1829-1841, September.
    6. Tsukuma, Hisayuki, 2016. "Estimation of a high-dimensional covariance matrix with the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 1-17.
    7. Bodnar, Taras & Okhrin, Yarema, 2008. "Properties of the singular, inverse and generalized inverse partitioned Wishart distributions," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2389-2405, November.
    8. Liu, Jin Shan & Ip, Wai Cheung & Wong, Heung, 2009. "Predictive inference for singular multivariate elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1440-1446, August.
    9. Díaz-García, José A., 2007. "A note about measures and Jacobians of singular random matrices," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 960-969, May.
    10. Bodnar, Taras & Mazur, Stepan & Podgórski, Krzysztof, 2016. "Singular inverse Wishart distribution and its application to portfolio theory," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 314-326.
    11. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2015. "Estimation of the mean vector in a singular multivariate normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 245-258.
    12. Díaz García, José A. & González Farías, Graciela, 2002. "Singular random matrix decompositions: Jacobians," DES - Working Papers. Statistics and Econometrics. WS ws024110, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Hisayuki Tsukuma & Tatsuya Kubokawa, 2014. "Estimation and Prediction Intervals in Transformed Linear Mixed Models," CIRJE F-Series CIRJE-F-930, CIRJE, Faculty of Economics, University of Tokyo.
    14. Frank G. Ball & Ian L. Dryden & Mousa Golalizadeh, 2008. "Brownian Motion and Ornstein–Uhlenbeck Processes in Planar Shape Space," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 1-22, March.
    15. Shimizu, Koki & Hashiguchi, Hiroki, 2021. "Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    16. Andrea Carriero & Francesco Corsello & Massimiliano Marcellino, 2020. "The economic drivers of volatility and uncertainty," Temi di discussione (Economic working papers) 1285, Bank of Italy, Economic Research and International Relations Area.
    17. Díaz-García, José A. & González-Farías, Graciela, 2005. "Singular random matrix decompositions: Jacobians," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 296-312, April.
    18. Díaz-García, José A. & Jáimez, Ramón Gutierrez & Mardia, Kanti V., 1997. "Wishart and Pseudo-Wishart Distributions and Some Applications to Shape Theory," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 73-87, October.
    19. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2016. "Unified improvements in estimation of a normal covariance matrix in high and low dimensions," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 233-248.
    20. Bodnar, Taras & Mazur, Stepan & Muhinyuza, Stanislas & Parolya, Nestor, 2017. "On the product of a singular Wishart matrix and a singular Gaussian vector in high dimensions," Working Papers 2017:7, Örebro University, School of Business.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:ws024211. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.