The statistics of cross-validation residuals - Theory
The statistics of cross-validation residuals - Theory
The expected values derived above are only applicable for correctly weighted
least-squares refinements. However 
has also been used to
optimise the weighting of geometrical or temperature factor terms in
refinement by adjusting the weights so as to minimise
(Brünger, 1992, 1993). It is therefore of interest to enquire how
responds to variations in weighting.
Appendix III shows that the weights 
which correctly reflect
experimental and model errors, minimise the variance of both the
refined parameters 
, and also the expected value of the
sum of the squares of the unweighted residuals in the test set. Hence
the choice of these weights approximately minimises . One
method of estimating such weights has been described by Tickle,
Laskowski & Moss (1998).
The statistics of cross-validation residuals - Theory