  Motivated by an open problem of validating protein identities in label-free
shotgun proteomics work-flows, we present a testing procedure to validate
class/protein labels using available measurements across instances/peptides.
More generally, we present a solution to the problem of identifying instances
that are deemed, based on some distance (or quasi-distance) measure, as
outliers relative to the subset of instances assigned to the same class. The
proposed procedure is non-parametric and requires no specific distributional
assumption on the measured distances. The only assumption underlying the
testing procedure is that measured distances between instances within the same
class are stochastically smaller than measured distances between instances from
different classes. The test is shown to simultaneously control the Type I and
Type II error probabilities whilst also controlling the overall error
probability of the repeated testing invoked in the validation procedure of
initial class labeling. The theoretical results are supplemented with results
from an extensive numerical study, simulating a typical setup for labeling
validation in proteomics work-flow applications. These results illustrate the
applicability and viability of our method. Even with up to 25% of instances
mislabeled, our testing procedure maintains a high specificity and greatly
reduces the proportion of mislabeled instances.
