IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v128y2017icp67-70.html
   My bibliography  Save this article

Multiplying a Gaussian matrix by a Gaussian vector

Author

Listed:
  • Mattei, Pierre-Alexandre

Abstract

We provide a new and simple characterization of the multivariate generalized Laplace distribution. In particular, our characterization implies that the product of a Gaussian matrix with independent and identically distributed columns and an independent isotropic Gaussian vector follows a symmetric multivariate generalized Laplace distribution.

Suggested Citation

  • Mattei, Pierre-Alexandre, 2017. "Multiplying a Gaussian matrix by a Gaussian vector," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 67-70.
    • Handle: RePEc:eee:stapro:v:128:y:2017:i:c:p:67-70
    DOI: 10.1016/j.spl.2017.04.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715217301359
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2017.04.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Mencía, Javier & Sentana, Enrique, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Journal of Econometrics, Elsevier, vol. 153(2), pages 105-121, December.
    3. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    4. Anderson, Dale N., 1992. "A multivariate Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 333-336, July.
    5. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
    6. Yu, Yaming, 2017. "On normal variance–mean mixtures," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 45-50.
    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. Yury Khokhlov & Victor Korolev & Alexander Zeifman, 2020. "Multivariate Scale-Mixed Stable Distributions and Related Limit Theorems," Mathematics, MDPI, vol. 8(5), pages 1-29, May.
    2. Paolella, Marc S. & Polak, Paweł, 2015. "COMFORT: A common market factor non-Gaussian returns model," Journal of Econometrics, Elsevier, vol. 187(2), pages 593-605.
    3. Steven Andrew Culpepper & Trevor Park, 2017. "Bayesian Estimation of Multivariate Latent Regression Models: Gauss Versus Laplace," Journal of Educational and Behavioral Statistics, , vol. 42(5), pages 591-616, October.
    4. Tomasz J. Kozubowski & Krzysztof Podgórski, 2000. "A Multivariate and Asymmetric Generalization of Laplace Distribution," Computational Statistics, Springer, vol. 15(4), pages 531-540, December.
    5. Bonhomme, Stphane & Robin, Jean-Marc, 2009. "Consistent noisy independent component analysis," Journal of Econometrics, Elsevier, vol. 149(1), pages 12-25, April.
    6. Li, Chunyu & Lou, Chenxin & Luo, Dan & Xing, Kai, 2021. "Chinese corporate distress prediction using LASSO: The role of earnings management," International Review of Financial Analysis, Elsevier, vol. 76(C).
    7. Mei Xing, 2017. "Existence Conditions of Super-Replication Cost in a Multinomial Model," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(4), pages 185-195, August.
    8. Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
    9. Armagan, Artin & Dunson, David, 2011. "Sparse variational analysis of linear mixed models for large data sets," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1056-1062, August.
    10. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    11. Mahmoud Zarepour & Thierry Bedard & Andre Dabrowski, 2008. "Return and Value at Risk using the Dirichlet Process," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(3), pages 205-218.
    12. Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    13. Martin Feldkircher & Florian Huber & Gary Koop & Michael Pfarrhofer, 2022. "APPROXIMATE BAYESIAN INFERENCE AND FORECASTING IN HUGE‐DIMENSIONAL MULTICOUNTRY VARs," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1625-1658, November.
    14. Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
    15. Eliaz, Kfir & Spiegler, Ran, 2022. "On incentive-compatible estimators," Games and Economic Behavior, Elsevier, vol. 132(C), pages 204-220.
    16. Samuel Asante Gyamerah & Philip Ngare & Dennis Ikpe, 2018. "Regime-Switching Temperature Dynamics Model for Weather Derivatives," International Journal of Stochastic Analysis, Hindawi, vol. 2018, pages 1-15, July.
    17. Ricardo Crisóstomo, 2021. "Estimating real‐world probabilities: A forward‐looking behavioral framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(11), pages 1797-1823, November.
    18. Kun Gao & Roger Lee, 2014. "Asymptotics of implied volatility to arbitrary order," Finance and Stochastics, Springer, vol. 18(2), pages 349-392, April.
    19. Fu, Qi & So, Jacky Yuk-Chow & Li, Xiaotong, 2024. "Stable paretian distribution, return generating processes and habit formation—The implication for equity premium puzzle," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    20. Oguzhan Cepni & I. Ethem Guney & Norman R. Swanson, 2020. "Forecasting and nowcasting emerging market GDP growth rates: The role of latent global economic policy uncertainty and macroeconomic data surprise factors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 18-36, January.

    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:eee:stapro:v:128:y:2017:i:c:p:67-70. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.