IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v137y2015icp32-49.html
   My bibliography  Save this article

Equivariant minimax dominators of the MLE in the array normal model

Author

Listed:
  • Gerard, David
  • Hoff, Peter

Abstract

Inference about dependence in a multiway data array can be made using the array normal model, which corresponds to the class of multivariate normal distributions with separable covariance matrices. Maximum likelihood and Bayesian methods for inference in the array normal model have appeared in the literature, but there have not been any results concerning the optimality properties of such estimators. In this article, we obtain results for the array normal model that are analogous to some classical results concerning covariance estimation for the multivariate normal model. We show that under a lower triangular product group, a uniformly minimum risk equivariant estimator (UMREE) can be obtained via a generalized Bayes procedure. Although this UMREE is minimax and dominates the MLE, it can be improved upon via an orthogonally equivariant modification. Numerical comparisons of the risks of these estimators show that the equivariant estimators can have substantially lower risks than the MLE.

Suggested Citation

  • Gerard, David & Hoff, Peter, 2015. "Equivariant minimax dominators of the MLE in the array normal model," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 32-49.
    • Handle: RePEc:eee:jmvana:v:137:y:2015:i:c:p:32-49
    DOI: 10.1016/j.jmva.2015.01.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15000330
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.01.020?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. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, January.
    2. Ohlson, Martin & Rauf Ahmad, M. & von Rosen, Dietrich, 2013. "The multilinear normal distribution: Introduction and some basic properties," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 37-47.
    3. James Zidek, 1969. "A representation of Bayes invariant procedures in terms of Haar measure," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 291-308, December.
    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. Hafner, C. M. & Linton, O., 2016. "Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case," Cambridge Working Papers in Economics 1664, Faculty of Economics, University of Cambridge.
    2. Hafner, Christian M. & Linton, Oliver B. & Tang, Haihan, 2020. "Estimation of a multiplicative correlation structure in the large dimensional case," Journal of Econometrics, Elsevier, vol. 217(2), pages 431-470.
    3. Paolo Giordani & Roberto Rocci & Giuseppe Bove, 2020. "Factor Uniqueness of the Structural Parafac Model," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 555-574, September.
    4. Christian M. Hafner & Oliver Linton & Haihan Tang, 2016. "Estimation of a multiplicative covariance structure in the large dimensional case," CeMMAP working papers 52/16, Institute for Fiscal Studies.

    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. Chen Tong & Peter Reinhard Hansen & Ilya Archakov, 2024. "Cluster GARCH," Papers 2406.06860, arXiv.org.
    2. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    3. Lamboni, Matieyendou, 2022. "Efficient dependency models: Simulating dependent random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 199-217.
    4. Christian M. Hafner & Oliver Linton & Haihan Tang, 2016. "Estimation of a multiplicative covariance structure in the large dimensional case," CeMMAP working papers 52/16, Institute for Fiscal Studies.
    5. Chen, Tao & Martin, Elaine & Montague, Gary, 2009. "Robust probabilistic PCA with missing data and contribution analysis for outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3706-3716, August.
    6. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.
    7. Hafner, Christian M. & Linton, Oliver B. & Tang, Haihan, 2020. "Estimation of a multiplicative correlation structure in the large dimensional case," Journal of Econometrics, Elsevier, vol. 217(2), pages 431-470.
    8. HAFNER, Christian & LINTON, Oliver B. & TANG, Haihan, 2016. "Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case," LIDAM Discussion Papers CORE 2016044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    10. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    11. Badi H. Baltagi & Georges Bresson & Anoop Chaturvedi & Guy Lacroix, 2022. "Robust Dynamic Space-Time Panel Data Models Using ε-contamination: An Application to Crop Yields and Climate Change," Center for Policy Research Working Papers 254, Center for Policy Research, Maxwell School, Syracuse University.
    12. Kociecki, Andrzej, 2012. "Orbital Priors for Time-Series Models," MPRA Paper 42804, University Library of Munich, Germany.
    13. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, January.
    14. Ricardo Leiva & Anuradha Roy, 2016. "Multi-level multivariate normal distribution with self-similar compound symmetry covariance matrix," Working Papers 0146mss, College of Business, University of Texas at San Antonio.
    15. A. El-Bassiouny & M. Jones, 2009. "A bivariate F distribution with marginals on arbitrary numerator and denominator degrees of freedom, and related bivariate beta and t distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(4), pages 465-481, November.
    16. Punzo, Antonio & Bagnato, Luca, 2022. "Dimension-wise scaled normal mixtures with application to finance and biometry," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    17. Domínguez-Molina, J. Armando & Rocha-Arteaga, Alfonso, 2007. "On the infinite divisibility of some skewed symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 77(6), pages 644-648, March.
    18. Chelsey Hill & James Li & Matthew J. Schneider & Martin T. Wells, 2021. "The tensor auto‐regressive model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 636-652, July.
    19. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    20. Arismendi, J.C., 2013. "Multivariate truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 41-75.

    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:137:y:2015:i:c:p:32-49. 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.