Title: Some properties of nested Kriging predictors,
Abstract: Kriging is a widely employed technique, in particular for computer
experiments, in machine learning or in geostatistics. An important challenge
for Kriging is the computational burden when the data set is large. We focus on
a class of methods aiming at decreasing this computational cost, consisting in
aggregating Kriging predictors based on smaller data subsets. We prove that
aggregations based solely on the conditional variances provided by the
different Kriging predictors can yield an inconsistent final Kriging
prediction. In contrasts, we study theoretically the recent proposal by
[Rulli{è}re et al., 2017] and obtain additional attractive properties for it.
We prove that this predictor is consistent, we show that it can be interpreted
as an exact conditional distribution for a modified process and we provide
error bounds for it.