  Canonical Correlation Analysis (CCA) is a method for analyzing pairs of
random vectors; it learns a sequence of paired linear transformations such that
the resultant canonical variates are maximally correlated within pairs while
uncorrelated across pairs. CCA outputs both canonical correlations as well as
the canonical directions which define the transformations. While inference for
canonical correlations is well developed, conducting inference for canonical
directions is more challenging and not well-studied, but is key to
interpretability. We propose a computational bootstrap method (combootcca) for
inference on CCA directions. We conduct thorough simulation studies that range
from simple and well-controlled to complex but realistic and validate the
statistical properties of combootcca while comparing it to several competitors.
We also apply the combootcca method to a brain imaging dataset and discover
linked patterns in brain connectivity and behavioral scores.
