  In many applications, we have access to the complete dataset but are only
interested in the prediction of a particular region of predictor variables. A
standard approach is to find the globally best modeling method from a set of
candidate methods. However, it is perhaps rare in reality that one candidate
method is uniformly better than the others. A natural approach for this
scenario is to apply a weighted $L_2$ loss in performance assessment to reflect
the region-specific interest. We propose a targeted cross-validation (TCV) to
select models or procedures based on a general weighted $L_2$ loss. We show
that the TCV is consistent in selecting the best performing candidate under the
weighted $L_2$ loss. Experimental studies are used to demonstrate the use of
TCV and its potential advantage over the global CV or the approach of using
only local data for modeling a local region.
  Previous investigations on CV have relied on the condition that when the
sample size is large enough, the ranking of two candidates stays the same.
However, in many applications with the setup of changing data-generating
processes or highly adaptive modeling methods, the relative performance of the
methods is not static as the sample size varies. Even with a fixed
data-generating process, it is possible that the ranking of two methods
switches infinitely many times. In this work, we broaden the concept of the
selection consistency by allowing the best candidate to switch as the sample
size varies, and then establish the consistency of the TCV. This flexible
framework can be applied to high-dimensional and complex machine learning
scenarios where the relative performances of modeling procedures are dynamic.
