Non-degenerate U-statistics for data missing completely at random with application to testing independence

Although the era of digitalization has enabled access to large quantities of data, due to their insufficient structuring, some data are often missing, and sometimes, the percentage of missing data is significant compared to the entire sample. On the other hand, most of the statistical methodology is designed for complete data. Here, we explore the asymptotic properties of non-degenerate U-statistics when the data are missing completely at random and a complete-case approach is utilized. The obtained results are applied to the estimator of Kendall's $tau$ used for testing independence. In this context, the median-based imputation approach is also considered, and asymptotic properties are explored. In addition, both complete-case and median imputation approaches are compared in an extensive Monte Carlo study.