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Sufficiency and completeness in the linear model

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  • Mueller, Jochen

Abstract

This paper provides further contributions to the theory of linear sufficiency and linear completeness. The notion of linear sufficiency was introduced by [2], Ann. Statist. 9, 913-916) and Drygas (in press, Sankhya) with respect to the linear model Ey = X[beta], var y = V. In addition to correcting an inadequate proof of [8], the relationship to an earlier definition and to the theory of linear prediction is also demonstrated. Moreover, the notion is extended to the model Ey = X[beta], var y = [delta]2V. Its connection with sufficiency under normality is investigated. An example illustrates the results.

Suggested Citation

  • Mueller, Jochen, 1987. "Sufficiency and completeness in the linear model," Journal of Multivariate Analysis, Elsevier, vol. 21(2), pages 312-323, April.
    • Handle: RePEc:eee:jmvana:v:21:y:1987:i:2:p:312-323
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    Citations

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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. Markiewicz, Augustyn, 1996. "Characterization of general ridge estimators," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 145-148, April.
    3. Liu, Xu-qing & Rong, Jian-ying, 2007. "Nonnegative quadratic estimation and quadratic sufficiency in general linear models," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1180-1194, July.
    4. Stepniak, C., 1997. "Sandwich theorem in comparison of multivariate normal experiments," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 281-284, May.
    5. 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.
    6. Markiewicz, Augustyn, 1998. "Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators," Statistics & Probability Letters, Elsevier, vol. 38(4), pages 347-354, July.
    7. 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.
    8. Liu, Xu-Qing & Wang, Dong-Dong & Rong, Jian-Ying, 2009. "Quadratic prediction and quadratic sufficiency in finite populations," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1979-1988, October.

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