# Article

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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 $\bold X$.