  This work falls within the context of predicting the value of a real function
at some input locations given a limited number of observations of this
function. The Kriging interpolation technique (or Gaussian process regression)
is often considered to tackle such a problem but the method suffers from its
computational burden when the number of observation points is large. We
introduce in this article nested Kriging predictors which are constructed by
aggregating sub-models based on subsets of observation points. This approach is
proven to have better theoretical properties than other aggregation methods
that can be found in the literature. Contrarily to some other methods it can be
shown that the proposed aggregation method is consistent. Finally, the
practical interest of the proposed method is illustrated on simulated datasets
and on an industrial test case with $10^4$ observations in a 6-dimensional
space.
