  A stochastic algorithm for the recursive approximation of the location
$\theta$ of a maximum of a regression function was introduced by Kiefer and
Wolfowitz [Ann. Math. Statist. 23 (1952) 462--466] in the univariate framework,
and by Blum [Ann. Math. Statist. 25 (1954) 737--744] in the multivariate case.
The aim of this paper is to provide a companion algorithm to the
Kiefer--Wolfowitz--Blum algorithm, which allows one to simultaneously
recursively approximate the size $\mu$ of the maximum of the regression
function. A precise study of the joint weak convergence rate of both algorithms
is given; it turns out that, unlike the location of the maximum, the size of
the maximum can be approximated by an algorithm which converges at the
parametric rate. Moreover, averaging leads to an asymptotically efficient
algorithm for the approximation of the couple $(\theta,\mu)$.
