<p>This paper concerns multivariate <i>U</i>-statistics which form a class of unbiased estimators for some multiparameter of interest. We propose an unbiased covariance matrix estimator for a multivariate <i>U</i>-statistic that can be utilized to perform hypothesis tests comparing multiple components of the target parameter vector simultaneously. In addition, we advocate the use of a partition-resampling scheme that can realize the proposed variance estimator with high computational efficiency. We demonstrate the effectiveness of the developed methodology through two simulation studies: multi-class classification using subsampling-based ensemble methods and mean comparison in a multivariate distribution. Furthermore, we illustrate the practical applications of the proposal using two real data examples that concern a handwriting digit classification problem and a longitudinal study on comparing two percent body fat measurements, respectively.</p>