Stochastic Approximation for Smooth Functions
Fabian, Vaclav
Ann. Math. Statist., Tome 40 (1969) no. 6, p. 299-302 / Harvested from Project Euclid
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The problem of approximating a point $\theta$ of minimum of a function $f \varepsilon \mathscr{C}$ (see 2.1) is considered. An approximation procedure of the type described in Fabian (1967) using the design described in Fabian (1968), but with the size of design increasing, achieves the speed \begin{equation*}\tag{1}E|X_n - \theta|^2 = o(t^{-1}_n \log ^3 t_n);\end{equation*} here $X_n$ is the $n$th approximation and $t_n$ the number of observations necessary to construct $X_1, X_2, \cdots, X_n$.
Publié le : 1969-02-14
Classification:  
@article{1177697825,
     author = {Fabian, Vaclav},
     title = {Stochastic Approximation for Smooth Functions},
     journal = {Ann. Math. Statist.},
     volume = {40},
     number = {6},
     year = {1969},
     pages = { 299-302},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177697825}
}

Fabian, Vaclav. Stochastic Approximation for Smooth Functions. Ann. Math. Statist., Tome 40 (1969) no. 6, pp.  299-302. http://gdmltest.u-ga.fr/item/1177697825/