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Linear sufficiency and some applications in multilinear estimation

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  • Drygas, Hilmar

Abstract

In the linear model Y = X[beta] + u the question arises when a linear transformation z = Ly contains all information of the linear model. This problem was solved by[2], Drygas (, forthcoming) and [11]). As an application the estimation of the variance of the observations, its skewness, and its kurtosis are considered. This is done by considering so-called derived models. ( [1], Fourth Berkeley Symp. Math. Statist. Prob. 1, 1-36; [14], Metrika 27, 103-113;[10], Math. Operationsforsch. Statist. Ser. Statist. 9, 443-478). Linear sufficient statistics are derived for these problems.

Suggested Citation

  • Drygas, Hilmar, 1985. "Linear sufficiency and some applications in multilinear estimation," Journal of Multivariate Analysis, Elsevier, vol. 16(1), pages 71-84, February.
    • Handle: RePEc:eee:jmvana:v:16:y:1985:i:1:p:71-84
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    Cited by:

    1. Dermoune, Azzouz & Rahmania, Nadji & Wei, Tianwen, 2012. "General linear mixed model and signal extraction problem with constraint," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 311-321.
    2. 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.
    3. Yongge Tian, 2017. "Transformation approaches of linear random-effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 583-608, November.
    4. Ohlson, Martin & Rauf Ahmad, M. & von Rosen, Dietrich, 2013. "The multilinear normal distribution: Introduction and some basic properties," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 37-47.
    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. 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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