A recently proposed modification to U-statistics shows how U-statistics could be evaluated in a semi-supervised setting. This present thesis’s objective is to apply this modification to U-statistics for dependence measures and to construct semi-supervised independence tests. Particular attention is called to the case of dependence measures whose U-statistics are degenerate under the null hypothesis of independence, and challenges relating to this are highlighted. The performance of these semi-supervised tests is compared to their unmodified counterparts, and the results confirm the improved power of tests using Kendall’s tau and the Pearson covariance, both non-degenerate dependence measures under the null hypothesis. For degenerate U-statistics, an oracle version of the semi-supervised U-statistic applied to the Distance Covariance by Székely, Rizzo, and Bakirov is considered. Due to the involved nature of this problem, simulation results were only obtained for small sample sizes, but despite the volatile nature of the results, they indicate potential improvements in power for higher sample sizes.     «

A recently proposed modification to U-statistics shows how U-statistics could be evaluated in a semi-supervised setting. This present thesis’s objective is to apply this modification to U-statistics for dependence measures and to construct semi-supervised independence tests. Particular attention is called to the case of dependence measures whose U-statistics are degenerate under the null hypothesis of independence, and challenges relating to this are highlighted. The performance of these semi-su...     »