  In this paper, we propose semiparametric efficient estimators of genetic
relatedness between two traits in a model-free framework. Most existing methods
require specifying certain parametric models involving the traits and genetic
variants. However, the bias due to model misspecification may yield misleading
statistical results. Moreover, the semiparametric efficient bounds for
estimators of genetic relatedness are still lacking. In this paper, we develop
semiparametric efficient estimators with machine learning methods and construct
valid confidence intervals for two important measures of genetic relatedness:
genetic covariance and genetic correlation, allowing both continuous and
discrete responses. Based on the derived efficient influence functions of
genetic relatedness, we propose a consistent estimator of the genetic
covariance as long as one of genetic values is consistently estimated. The data
of two traits may be collected from the same group or different groups of
individuals. Various numerical studies are performed to illustrate our
introduced procedures. We also apply proposed procedures to analyze Carworth
Farms White mice genome-wide association study data.
