Consider the family of bivariate distributionsFX,Yfrom which we have an iid set of observationsVi= (Xi, Yi), i= 1, . . . , n. We want to estimate the covariance betweenXandY, i.e.,XY=E[XY]E[X]E[Y]. What is the kernel and what is its degree? Using these to show that the U-statistic for the estimator is given by

[(Xi-Xbar)(Yi-Ybar)]/(n-1)

the "unbiased sample covariance".