  This article studies a Newton-like method already used by several authors but
which has not been thouroughly studied yet. We call it the robust-variance
scoring (RVS) algorithm because the main version of the algorithm that we
consider replaces minus the Hessian of the loglikelihood used in the
Newton-Raphson algorithm by a matrix $G$ which is an estimate of the variance
of the score under the true probability, which uses only the individual scores.
Thus an iteration of this algorithm requires much less computations than an
iteration of the Newton-Raphson algorithm. Moreover this estimate of the
variance of the score estimates the information matrix at maximum. We have also
studied a convergence criterion which has the nice interpretation of estimating
the ratio of the approximation error over the statistical error; thus it can be
used for stopping the iterative process whatever the problem. A simulation
study confirms that the RVS algorithm is faster than the Marquardt algorithm (a
robust version of the Newton-Raphson algorithm); this happens because the
number of iterations needed by the RVS algorithm is barely larger than that
needed by the Marquardt algorithm while the computation time for each iteration
is much shorter. Also the coverage rates using the matrix $G$ are satisfactory.
