Estimation of distribution functions and quantiless with missing data

A distribution-free imputation procedure based on nonparametric kernel regression is proposed to estimate the distribution function and quantiles of a random variable that is incompletely observed. Assuming the baseline missing-at-random model for nonrespondence, we discuss consistent estimation via estimating the conditional distribution by the kernel method. A strong uniform convergence rate comparable to that of density estimation is proved. We derive asymptotic normality for estimating the cdf and the quantile via establishing the mean square consistency and the asymptotically optimal band width selection. A simulation study compares the proposed nonparametric method with the naive pairwise deletion method and a linear regression method under a parametric linear model.