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Estimation of a quadratic function of the parameter of the mean in a linear model
Applications of Mathematics, Tome 34 (1989) no. 2, pp. 155-160
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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 $\bold X$.
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 $\bold X$.
DOI : 10.21136/AM.1989.104343
Classification : 62F10, 62H12, 62J05
Keywords: best unbiased quadratic estimator; quadratic function; best unbiased estimator; linear model 
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Volaufová, Júlia; Volauf, Peter. Estimation of a quadratic function of the parameter of the mean in a linear model. Applications of Mathematics, Tome 34 (1989) no. 2, pp. 155-160. doi: 10.21136/AM.1989.104343

[1] J. Kleffe: Simultaneous Estimation of Expectation and Covariance Matrix in Linear Models. Math. Operationsforsch. Statist., Ser. Statistics, Vol. 9 (1978) No. 3, 443-478. | MR | Zbl

[2] J. Volaufová: Estimation of Polynomials in the Regression Model. Aplikace matematiky, Vol. 27 (1982), No. 3, 223-231. | MR

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