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Linear sufficiency and linear admissibility in a continuous time Gauss-Markov model

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  • Ibarrola, P.
  • Pérez-Palomares, A.

Abstract

This paper considers the problem of estimation in a linear model when a stochastic process instead of a random vector is observed. Estimators obtained as integrals of the observed process are studied. Characterizations of linear sufficiency and admissibility similar to those given in the classical linear model are obtained in this context. Moreover, a definition of generalized ridge estimators in continuous time is introduced and also a characterization of such estimators is given.

Suggested Citation

  • Ibarrola, P. & Pérez-Palomares, A., 2003. "Linear sufficiency and linear admissibility in a continuous time Gauss-Markov model," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 315-327, November.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:2:p:315-327
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    References listed on IDEAS

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    1. Wu, Tiee-Jian & Wasan, M. T., 1996. "Weighted least squares estimates in linear regression models for processes with uncorrelated increments," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 273-286, November.
    2. Markiewicz, Augustyn, 1996. "Characterization of general ridge estimators," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 145-148, April.
    3. Le Breton, A. & Musiela, M., 1987. "Strong consistency of least squares estimates in linear regression models driven by semimartingales," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 77-92, October.
    4. Mueller, Jochen, 1987. "Sufficiency and completeness in the linear model," Journal of Multivariate Analysis, Elsevier, vol. 21(2), pages 312-323, April.
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    Cited by:

    1. Ibarrola, P. & Pérez-Palomares, A., 2004. "Linear completeness in a continuous time Gauss-Markov model," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 143-149, August.
    2. Chaigneau, Pierre, 2018. "The optimal timing of CEO compensation," Finance Research Letters, Elsevier, vol. 24(C), pages 90-94.
    3. Liu, Xu-Qing & Rong, Jian-Ying & Liu, Xiu-Ying, 2008. "Best linear unbiased prediction for linear combinations in general mixed linear models," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1503-1517, September.

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