  This paper deals with probabilistic upper bounds for the error in functional
estimation defined on some interpolation and extrapolation designs, when the
function to estimate is supposed to be analytic. The error pertaining to the
estimate may depend on various factors: the frequency of observations on the
knots, the position and number of the knots, and also on the error committed
when approximating the function through its Taylor expansion. When the number
of observations is fixed, then all these parameters are determined by the
choice of the design and by the choice estimator of the unknown function. The
scope of the paper is therefore to determine a rule for the minimal number of
observation required to achieve an upper bound of the error on the estimate
with a given maximal probability.
