Lower Rate of Convergence for Locating a Maximum of a Function
Chen, Hung
Ann. Statist., Tome 16 (1988) no. 1, p. 1330-1334 / Harvested from Project Euclid
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The problem is considered of estimating the point of global maximum of a function $f$ belonging to a class $F$ of functions on $\lbrack -1, 1 \rbrack,$ based on estimates of function values at points selected possibly during the experimentation. If $p$ is odd and greater than 1, $K$ is a positive constant and $F$ contains enough functions with $p$th derivatives bounded by $K$, then we prove that, under additional weak regularity conditions, the lower rate of convergence is $n^{-(p - 1)/(2p)}$.
Publié le : 1988-09-14
Classification:  Rate of convergence,  global maximum,  62G99,  62L20 
@article{1176350965,
     author = {Chen, Hung},
     title = {Lower Rate of Convergence for Locating a Maximum of a Function},
     journal = {Ann. Statist.},
     volume = {16},
     number = {1},
     year = {1988},
     pages = { 1330-1334},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350965}
}

Chen, Hung. Lower Rate of Convergence for Locating a Maximum of a Function. Ann. Statist., Tome 16 (1988) no. 1, pp.  1330-1334. http://gdmltest.u-ga.fr/item/1176350965/