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Linear sufficiency with respect to a given vector of parametric functions. (English) Zbl 0614.62079

Let \(\{\) Y,X\(\beta\),V\(\}\) be a general Gauss-Markov model. FY is said to be linearly sufficient for the estimable function \(K\beta\) if the minimum dispersion linear unbiased estimator of \(K\beta\) is a linear function of FY. Theorem 1 gives a necessary and sufficient condition for such a linear sufficiency. Corollaries deal with some special cases, while theorem 2 considers the problem of linear minimal sufficiency. Applications are given to models with additional information on nuisance parameters, stepwise estimation and seemingly unrelated regressions.
Reviewer: H.Caussinus

MSC:

62J05 Linear regression; mixed models
62B05 Sufficient statistics and fields
62F10 Point estimation
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References:

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