Geodesic
On weighted polynomial regression designs with minimum average veriance
Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 734-738 
M. B. Malyutov; V. V. Fëdorov. On weighted polynomial regression designs with minimum average veriance. Teoriâ veroâtnostej i ee primeneniâ, Tome 16 (1971) no. 4, pp. 734-738. http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a15/
@article{TVP_1971_16_4_a15,
     author = {M. B. Malyutov and V. V. F\"edorov},
     title = {On weighted polynomial regression designs with minimum average veriance},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {734--738},
     year = {1971},
     volume = {16},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1971_16_4_a15/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let the measurements of the function $\eta(x)=(w(x))^{1/2}\sum_{\alpha=0}^m\theta_\alpha x^\alpha$ at points $x_i$ $i=1,\dots,N$ give the values $y_i=\eta(x_i)+\nu_i$, $\nu_i$ being independent random variables, $\mathbf E\nu_i=0$, $\mathbf D\nu_i=\sigma^2$. The design of the experiment can be described by a discrete probability measure $\varepsilon(x)$ which is the proportion of measurements at $x$. Let $d(x,\varepsilon)$ be the variance of the least-squares estimate $\widehat\eta(x)$ of the function $\eta(x)$. The unique designs of the experiment minimizing $$ a(\varepsilon)=\int_Xd(x,\varepsilon)\,dx $$ are found in the two cases: 1) $w(x)\equiv1$, $X=[-1,1]$ and 2) $w(x)=e^{-x^2}$, $X=(-\infty,\infty)$.