  Mantel's test (MT) for association is conducted by testing the linear
relationship of similarity of all pairs of subjects between two observational
domains. Motivated by applications to neuroimaging and genetics data, and
following the succes of shrinkage and kernel methods for prediction with
high-dimensional data, we here introduce the adaptive Mantel test as an
extension of the MT. By utilizing kernels and penalized similarity measures,
the adaptive Mantel test is able to achieve higher statistical power relative
to the classical MT in many settings. Furthermore, the adaptive Mantel test is
designed to simultaneously test over multiple similarity measures such that the
correct type I error rate under the null hypothesis is maintained without the
need to directly adjust the significance threshold for multiple testing. The
performance of the adaptive Mantel test is evaluated on simulated data, and is
used to investigate associations between genetics markers related to
Alzheimer's Disease and heatlhy brain physiology with data from a working
memory study of 350 college students from Beijing Normal University.
