IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v134y2015icp82-98.html
   My bibliography  Save this article

Robust linear functional mixed models

Author

Listed:
  • Riquelme, Marco
  • Bolfarine, Heleno
  • Galea, Manuel

Abstract

In this paper we propose a linear functional model with normal random effects and elliptical errors, thus extending the standard normal models considered previously. The corrected score approach (Nakamura, 1990) is used for parameter estimation and the resulting estimators are shown to be consistent and asymptotically normal. The local influence approach (Cook, 1986) is used for assessing influence of small perturbations on the parameter estimates. A simulation study is presented illustrating the good performance of the proposed approach, including the robustness property for the heavier tail models.

Suggested Citation

  • Riquelme, Marco & Bolfarine, Heleno & Galea, Manuel, 2015. "Robust linear functional mixed models," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 82-98.
    • Handle: RePEc:eee:jmvana:v:134:y:2015:i:c:p:82-98
    DOI: 10.1016/j.jmva.2014.10.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X14002358
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2014.10.008?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. Xu-Ping Zhong & Wing-Kam Fung & Bo-Cheng Wei, 2002. "Estimation in Linear Models with Random Effects and Errors-in-Variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 595-606, September.
    2. Reinaldo B. Arellano-Valle & Javier E. Contreras-Reyes & Marc G. Genton, 2013. "Shannon Entropy and Mutual Information for Multivariate Skew-Elliptical Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 42-62, March.
    3. Xu-Ping Zhong & Bo-Cheng Wei & Wing-Kam Fung, 2000. "Influence Analysis for Linear Measurement Error Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 367-379, June.
    4. Giménez, Patricia & Galea, Manuel, 2013. "Influence measures on corrected score estimators in functional heteroscedastic measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 1-15.
    5. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2009. "On estimation and influence diagnostics for the Grubbs' model under heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1249-1263, February.
    6. Vilca-Labra, F. & Arellano-Valle, R. B. & Bolfarine, H., 1998. "Elliptical Functional Models," Journal of Multivariate Analysis, Elsevier, vol. 65(1), pages 36-57, April.
    7. Xihong Lin & Raymond J. Carroll, 1999. "SIMEX Variance Component Tests in Generalized Linear Mixed Measurement Error Models," Biometrics, The International Biometric Society, vol. 55(2), pages 613-619, June.
    8. Casanova, María P. & Iglesias, Pilar & Bolfarine, Heleno & Salinas, Victor H. & Peña, Alexis, 2010. "Semiparametric Bayesian measurement error modeling," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 512-524, 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. Danilo Leal & Rodrigo Jiménez & Marco Riquelme & Víctor Leiva, 2023. "Elliptical Capital Asset Pricing Models: Formulation, Diagnostics, Case Study with Chilean Data, and Economic Rationale," Mathematics, MDPI, vol. 11(6), pages 1-27, March.
    2. Joelmir A. Borssoi & Gilberto A. Paula & Manuel Galea, 2020. "Elliptical linear mixed models with a covariate subject to measurement error," Statistical Papers, Springer, vol. 61(1), pages 31-69, February.

    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. Karim Zare & Abdolrahman Rasekh & Ali Rasekhi, 2012. "Estimation of variance components in linear mixed measurement error models," Statistical Papers, Springer, vol. 53(4), pages 849-863, November.
    2. Christian Caamaño-Carrillo & Javier E. Contreras-Reyes, 2022. "A Generalization of the Bivariate Gamma Distribution Based on Generalized Hypergeometric Functions," Mathematics, MDPI, vol. 10(9), pages 1-17, May.
    3. Galea, Manuel & de Castro, Mário, 2017. "Robust inference in a linear functional model with replications using the t distribution," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 134-145.
    4. Camila Zeller & Victor Lachos & Filidor Labra, 2014. "Influence diagnostics for Grubbs’s model with asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 55(3), pages 671-690, August.
    5. Kheradmandi, Ameneh & Rasekh, Abdolrahman, 2015. "Estimation in skew-normal linear mixed measurement error models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 1-11.
    6. Joelmir A. Borssoi & Gilberto A. Paula & Manuel Galea, 2020. "Elliptical linear mixed models with a covariate subject to measurement error," Statistical Papers, Springer, vol. 61(1), pages 31-69, February.
    7. Manuel Galea & Patricia Giménez, 2019. "Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model," Statistical Papers, Springer, vol. 60(1), pages 293-312, February.
    8. Chunzheng Cao & Mengqian Chen & Yahui Wang & Jian Qing Shi, 2018. "Heteroscedastic replicated measurement error models under asymmetric heavy-tailed distributions," Computational Statistics, Springer, vol. 33(1), pages 319-338, March.
    9. Cui, Hengjian & Ng, Kai W. & Zhu, Lixing, 2004. "Estimation in mixed effects model with errors in variables," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 53-73, October.
    10. Dione Valença & Heleno Bolfarine, 2006. "Testing Homogeneity in Weibull Error in Variables Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(1), pages 115-129, March.
    11. Contreras-Reyes, Javier E. & Kharazmi, Omid, 2023. "Belief Fisher–Shannon information plane: Properties, extensions, and applications to time series analysis," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    12. Wenhui Liu & Zhonghua Li & Zhaojun Wang, 2022. "Monitoring of Linear Profiles Using Linear Mixed Model in the Presence of Measurement Errors," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    13. Arellano-Valle, Reinaldo B. & Bolfarine, Heleno & Gasco, Loreta, 2002. "Measurement Error Models with Nonconstant Covariance Matrices," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 395-415, August.
    14. Polzehl, Jorg & Zwanzig, Silvelyn, 2004. "On a symmetrized simulation extrapolation estimator in linear errors-in-variables models," Computational Statistics & Data Analysis, Elsevier, vol. 47(4), pages 675-688, November.
    15. Yi Li & Xihong Lin, 2003. "Testing the Correlation for Clustered Categorical and Censored Discrete Time-to-Event Data When Covariates Are Measured without/with Errors," Biometrics, The International Biometric Society, vol. 59(1), pages 25-35, March.
    16. Shi, Jianhong & Chen, Kun & Song, Weixing, 2014. "Robust errors-in-variables linear regression via Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 113-120.
    17. Mêgnigbêto, Eustache, 2014. "Efficiency, unused capacity and transmission power as indicators of the Triple Helix of university–industry–government relationships," Journal of Informetrics, Elsevier, vol. 8(1), pages 284-294.
    18. Camila Zeller & Rignaldo Carvalho & Victor Lachos, 2012. "On diagnostics in multivariate measurement error models under asymmetric heavy-tailed distributions," Statistical Papers, Springer, vol. 53(3), pages 665-683, August.
    19. Dima, Bogdan & Dima, Ştefana Maria, 2017. "Mutual information and persistence in the stochastic volatility of market returns: An emergent market example," International Review of Economics & Finance, Elsevier, vol. 51(C), pages 36-59.
    20. Zeller, Camila B. & Labra, Filidor V. & Lachos, Victor H. & Balakrishnan, N., 2010. "Influence analyses of skew-normal/independent linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1266-1280, May.

    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:134:y:2015:i:c:p:82-98. 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.