IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v165y2018icp14-26.html
   My bibliography  Save this article

The joint projected normal and skew-normal: A distribution for poly-cylindrical data

Author

Listed:
  • Mastrantonio, Gianluca

Abstract

This paper introduces a multivariate circular–linear (or poly-cylindrical) distribution obtained by combining the projected and the skew-normal. We show the flexibility of our proposal, its closure under marginalization, and how to quantify multivariate dependence. Due to a non-identifiability issue that our proposal inherits from the projected normal, a computational problem arises. We overcome it in a Bayesian framework, adding suitable latent variables and showing that posterior samples can be obtained with a post-processing of the estimation algorithm output. Under specific prior choices, this approach enables us to implement a Markov chain Monte Carlo algorithm relying only on Gibbs steps, where the updates of the parameters are done as if we were working with a multivariate normal likelihood. The proposed approach can also be used with the projected normal. As a proof of concept, on simulated examples we show the ability of our algorithm in recovering the parameter values and to solve the identification problem. Then the proposal is used in a real data example, where the turning-angles (circular variables) and the logarithm of the step-lengths (linear variables) of four zebras are modeled jointly.

Suggested Citation

  • Mastrantonio, Gianluca, 2018. "The joint projected normal and skew-normal: A distribution for poly-cylindrical data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 14-26.
    • Handle: RePEc:eee:jmvana:v:165:y:2018:i:c:p:14-26
    DOI: 10.1016/j.jmva.2017.11.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X17301069
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2017.11.006?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. Neveka Olmos & Héctor Varela & Héctor Gómez & Heleno Bolfarine, 2012. "An extension of the half-normal distribution," Statistical Papers, Springer, vol. 53(4), pages 875-886, November.
    2. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    3. Fangpo Wang & Alan E. Gelfand, 2014. "Modeling Space and Space-Time Directional Data Using Projected Gaussian Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1565-1580, December.
    4. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    5. R.B. Arellano-Valle & H. Bolfarine & V.H. Lachos, 2007. "Bayesian Inference for Skew-normal Linear Mixed Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(6), pages 663-682.
    6. Abe, Toshihiro & Ley, Christophe, 2017. "A tractable, parsimonious and flexible model for cylindrical data, with applications," Econometrics and Statistics, Elsevier, vol. 4(C), pages 91-104.
    7. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
    8. Gupta, Arjun K. & González-Farías, Graciela & Domínguez-Molina, J. Armando, 2004. "A multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 181-190, April.
    9. Kai-Florian Storch & Ovidiu Lipan & Igor Leykin & N. Viswanathan & Fred C. Davis & Wing H. Wong & Charles J. Weitz, 2002. "Extensive and divergent circadian gene expression in liver and heart," Nature, Nature, vol. 417(6884), pages 78-83, May.
    10. Anderson-Cook, C. M., 1997. "An extension to modeling cylindrical variables," Statistics & Probability Letters, Elsevier, vol. 35(3), pages 215-223, October.
    11. Gianluca Mastrantonio & Antonello Maruotti & Giovanna Jona‐Lasinio, 2015. "Bayesian hidden Markov modelling using circular‐linear general projected normal distribution," Environmetrics, John Wiley & Sons, Ltd., vol. 26(2), pages 145-158, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marc Hallin & H Lui & Thomas Verdebout, 2022. "Nonparametric Measure-transportation-based Methods for Directional Data," Working Papers ECARES 2022-18, ULB -- Universite Libre de Bruxelles.

    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. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.
    2. 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.
    3. Jenny Brynjarsdottir & Jonathan Hobbs & Amy Braverman & Lukas Mandrake, 2018. "Optimal Estimation Versus MCMC for $$\mathrm{{CO}}_{2}$$ CO 2 Retrievals," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 297-316, June.
    4. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87.
    5. Nico Keilman, 2020. "Evaluating Probabilistic Population Forecasts," Economie et Statistique / Economics and Statistics, Institut National de la Statistique et des Etudes Economiques (INSEE), issue 520-521, pages 49-64.
    6. Nowotarski, Jakub & Weron, Rafał, 2018. "Recent advances in electricity price forecasting: A review of probabilistic forecasting," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 1548-1568.
    7. Robu, Valentin & Chalkiadakis, Georgios & Kota, Ramachandra & Rogers, Alex & Jennings, Nicholas R., 2016. "Rewarding cooperative virtual power plant formation using scoring rules," Energy, Elsevier, vol. 117(P1), pages 19-28.
    8. Malte Knüppel & Fabian Krüger, 2022. "Forecast uncertainty, disagreement, and the linear pool," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(1), pages 23-41, January.
    9. Bansal, Prateek & Krueger, Rico & Graham, Daniel J., 2021. "Fast Bayesian estimation of spatial count data models," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    10. Theo S. Eicher & Chris Papageorgiou & Adrian E. Raftery, 2011. "Default priors and predictive performance in Bayesian model averaging, with application to growth determinants," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 30-55, January/F.
    11. de Haan, Thomas, 2020. "Eliciting belief distributions using a random two-level partitioning of the state space," Working Papers in Economics 1/20, University of Bergen, Department of Economics.
    12. Matteo Iacopini & Francesco Ravazzolo & Luca Rossini, 2020. "Proper scoring rules for evaluating asymmetry in density forecasting," Papers 2006.11265, arXiv.org, revised Sep 2020.
    13. Song, Haiyan & Wen, Long & Liu, Chang, 2019. "Density tourism demand forecasting revisited," Annals of Tourism Research, Elsevier, vol. 75(C), pages 379-392.
    14. Luisa Bisaglia & Matteo Grigoletto, 2021. "A new time-varying model for forecasting long-memory series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 139-155, March.
    15. Tomás Marinozzi, 2023. "Forecasting Inflation in Argentina: A Probabilistic Approach," Ensayos Económicos, Central Bank of Argentina, Economic Research Department, vol. 1(81), pages 81-110, May.
    16. Marczak, Martyna & Proietti, Tommaso & Grassi, Stefano, 2018. "A data-cleaning augmented Kalman filter for robust estimation of state space models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 107-123.
    17. Fabian Kruger & Hendrik Plett, 2022. "Prediction intervals for economic fixed-event forecasts," Papers 2210.13562, arXiv.org, revised Mar 2024.
    18. Yael Grushka-Cockayne & Kenneth C. Lichtendahl Jr. & Victor Richmond R. Jose & Robert L. Winkler, 2017. "Quantile Evaluation, Sensitivity to Bracketing, and Sharing Business Payoffs," Operations Research, INFORMS, vol. 65(3), pages 712-728, June.
    19. Krüger, Fabian & Nolte, Ingmar, 2016. "Disagreement versus uncertainty: Evidence from distribution forecasts," Journal of Banking & Finance, Elsevier, vol. 72(S), pages 172-186.
    20. André Victor Ribeiro Amaral & Elias Teixeira Krainski & Ruiman Zhong & Paula Moraga, 2024. "Model-Based Geostatistics Under Spatially Varying Preferential Sampling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 29(4), pages 766-792, December.

    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:jmvana:v:165:y:2018:i:c:p:14-26. 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.