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Robust linear functional mixed models

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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    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.

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