This article considers a distribution-free estimation procedure for a basic pattern of missing data that often arises from the wellknown double sampling in survey methodology. Without parametric modeling of the missing mechanism or the joint distribution, kernel regression estimators are used to estimate mean functionals through empirical estimation of the missing pattern. A generalization of the method of Cheng and Wei is verified under the assumption of missing at random. Asymptotic distributions are derived for estimating the mean of the incomplete data and for estimating the mean treatment difference in a nonrandomized observational study. The nonparametric method is compared with a naive pairwise deletion method and a linear regression method via the asymptotic relative efficiencies and a simulation study. The comparison shows that the proposed nonparametric estimators attain reliable performances in general.