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Locally best quadratic estimators. (English) Zbl 0597.62050
The n-dimensional column vector Y is observed, where $$Y=Xb+e$$, with X a known n by k matrix, b an unknown k-dimensional vector of parameters, and e an error vector with zero means and covariance matrix $$\sum^{p}_{i=1}\theta_ iV_ i$$, where $$V_ 1,...,V_ p$$ are known symmetric matrices and $$\theta_ 1,...,\theta_ p$$ are unknown parameters. The third and fourth central moments of the elements of the error vector e are given. The problem is to estimate $c_ 1b_ 1+...+c_ kb_ k+f_ 1\theta_ 1+...+f_ p\theta_ p,$ where $$c_ 1,...,c_ k$$, $$f_ 1,...,f_ p$$ are given values. The estimator is to be of the form $$a'Y+Y'AY$$ where a is an n-dimensional column vector and A is an n by n matrix. Explicit expressions are developed for a and A which give an unbiased estimator which has minimum variance at a specified parameter point.
Reviewer: L.Weiss

##### MSC:
 62H12 Estimation in multivariate analysis 62F10 Point estimation 62J05 Linear regression; mixed models
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##### References:
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