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Zbl 0597.62050
Kubáček, Lubomír
(English)
[J] Math. Slovaca 35, 393-408 (1985). ISSN 0139-9918; ISSN 1337-2211/e

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 $\sum\sp{p}\sb{i=1}\theta\sb iV\sb i$, where $V\sb 1,...,V\sb p$ are known symmetric matrices and $\theta\sb 1,...,\theta\sb p$ are unknown parameters. The third and fourth central moments of the elements of the error vector e are given. The problem is to estimate $$c\sb 1b\sb 1+...+c\sb kb\sb k+f\sb 1\theta\sb 1+...+f\sb p\theta\sb p,$$ where $c\sb 1,...,c\sb k$, $f\sb 1,...,f\sb p$ 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.
[L.Weiss]
MSC 2000:
*62H12 Multivariate estimation
62F10 Point estimation
62J05 Linear regression

Keywords: locally best quadratic estimators; tensor product; vec operator; higher order central moments; locally unbiased minimum variance; estimator; locally UMVUE; Explicit expressions

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