Geodesic
On estimating functions of the mean
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 3, pp. 573-577

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An estimation problem is considered for a function $\varphi(\alpha_1,\dots,\alpha_N)$ of unknown complex parameters $\alpha_1,\dots,\alpha_N$ by observations $\xi(t)=\alpha_1\theta_1(t)+\dots+\alpha_N\theta_N(t)+\Delta(t)$, $t\in T$, where $\Delta(t)$ is complex Gaussian stochastic function. The main result is: the best unbiased estimate of an analytic function $\varphi(\alpha_1,\dots,\alpha_N)$ is $\varphi(\widehat\alpha_1,\dots,\widehat\alpha_N)$ where $\widehat\alpha_k$ are the BLUE of regression coeffitients $\alpha_k$. The real-valued case and the case of infinite dimensional regression are briefly discussed. 
@article{TVP_1972_17_3_a16,
     author = {A. S. Kholevo},
     title = {On estimating functions of the mean},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {573--577},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_3_a16/}
}
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A. S. Kholevo. On estimating functions of the mean. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 3, pp. 573-577. http://geodesic.mathdoc.fr/item/TVP_1972_17_3_a16/