  In genome-wide interaction studies, to detect gene-gene interactions, most
methods are divided into two folds: single nucleotide polymorphisms (SNP) based
and gene-based methods. Basically, the methods based on the gene are more
effective than the methods based on a single SNP. Recent years, while the
kernel canonical correlation analysis (Classical kernel CCA) based U statistic
(KCCU) has proposed to detect the nonlinear relationship between genes. To
estimate the variance in KCCU, they have used resampling based methods which
are highly computationally intensive. In addition, classical kernel CCA is not
robust to contaminated data. We, therefore, first discuss robust kernel mean
element, the robust kernel covariance, and cross-covariance operators. Second,
we propose a method based on influence function to estimate the variance of the
KCCU. Third, we propose a nonparametric robust KCCU method based on robust
kernel CCA, which is designed for contaminated data and less sensitive to noise
than classical kernel CCA. Finally, we investigate the proposed methods to
synthesized data and imaging genetic data set. Based on gene ontology and
pathway analysis, the synthesized and genetics analysis demonstrate that the
proposed robust method shows the superior performance of the state-of-the-art
methods.
