Limit theorems for conditional U-statistics analysis on hyperspheres for missing at random data in the presence of measurement error

Missing data and measurement errors are prevalent challenges in modern statistical analyses, mainly when observations lie on complex structures like unit hyperspheres. To address these issues, we introduce a comprehensive framework for conditional U-statistics of general order, tailored explicitly for data missing at random and contaminated by measurement errors in such settings. We propose a novel deconvolution method for these conditional U-statistics and, for the first time, investigate its convergence rate and asymptotic distribution. Our unified approach establishes general asymptotic properties under broad model conditions, enabling us to derive asymptotic confidence intervals based on the estimator’s distribution. To demonstrate the practical significance of our framework, we provide new insights into the Kendall rank correlation coefficient and address discrimination problems.