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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

62H12 Estimation in multivariate analysis
62F10 Point estimation
62J05 Linear regression; mixed models
Full Text: EuDML
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