Asymptotic results for some U- and V-statistics for model specification testing under missing data

Abstract

Missing data issues are a common problem in practice. Although numerous model specification tests have been proposed for complete data, the literature addressing incomplete data remains sparse. Seeking to fill this gap, we focus on nondegenerate U- and V-statistics, with the ultimate goal of applying them in the context of independence testing via the well-known Kendall’s tau statistic. We assume that the data are Missing Completely At Random (MCAR). For general U- and V-statistics, we present their limiting distributions under the complete-case approach. For the specific case of Kendall’s tau, we provide additional results under median imputation and outline the path toward deriving analogous results for other commonly used imputation algorithms.