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Elliptical Functional Models

Author

Listed:
  • Vilca-Labra, F.
  • Arellano-Valle, R. B.
  • Bolfarine, H.

Abstract

In this paper, functional models with not replications are investigated within the class of the elliptical distributions. Emphasis is placed on the special case of the Student-t distribution. Main results encompasses consistency and asymptotic normality of the maximum likelihood estimators. Due to the presence of incidental parameters, standard maximum likelihood methodology cannot be used to obtain the main results, which require extensions of some existing results related to elliptical distributions. Asymptotic relative efficiencies are reported which show that the generalized least squares estimator can be highly inefficient when compared with the maximum likelihood estimator under nonnormality.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:65:y:1998:i:1:p:36-57
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    References listed on IDEAS

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    1. Lieftinck-Koeijers, C. A. J., 1988. "Multivariate calibration: A generalization of the classical estimator," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 31-44, April.
    2. Kubokawa, T. & Robert, C. P., 1994. "New Perspectives on Linear Calibration," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 178-200, October.
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    Cited by:

    1. Riquelme, Marco & Bolfarine, Heleno & Galea, Manuel, 2015. "Robust linear functional mixed models," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 82-98.
    2. 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.
    3. 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.
    4. 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.

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