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Estimation of a quadratic function of the parameter of the mean in a linear model. (English) Zbl 0673.62053

Summary: The paper deals with an optimal estimation of the quadratic function \(\beta 'D\beta\), where \(\beta \in {\mathbb{R}}^ k\), D is a known \(k\times k\) matrix, in the model \((Y,X\beta,\sigma^ 2I)\). The distribution of 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 X.

MSC:

62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
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References:

[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. · Zbl 0415.62026 · doi:10.1080/02331887808801444
[2] J. Volaufová: Estimation of Polynomials in the Regression Model. Aplikace matematiky, Vol. 27 (1982), No. 3, 223-231.
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