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best unbiased quadratic estimator; quadratic function; best unbiased estimator; linear model
The paper deals with an optimal estimation of the quadratic function $\bold{\beta'D\beta}$, where $\beta \in \Cal R^k, \bold D$ is a known $k \times k$ matrix, in the model $\bold{Y, X\beta, \sigma^2I}$. The distribution of $\bold Y$ is assumed to be symmetric and to have a finite fourth moment. An explicit form of the best unbiased estimator is given for a special case of the matrix $\bold X$.
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[2] J. Volaufová: Estimation of Polynomials in the Regression Model. Aplikace matematiky, Vol. 27 (1982), No. 3, 223-231. MR 0658004
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