Imputation methods for quantile estimation under missing at random

Imputation is frequently used to handle missing data for which multiple imputation is a popular technique. We propose a fractional hot deck imputation which produces a valid variance estimator for quantiles. In the proposed method, the imputed values are chosen from the set of respondents and are assigned with proper fractional weights that use a density function for the working model. In addition, we consider a nonparametric fractional imputation method based on nonparametric kernel regression, avoiding a parametric distribution assumption and thus giving more robustness. The resulting estimator can be called nonparametric fractionally imputation estimator. Valid variance estimation is also discussed. A limited simulation study compares the proposed methods favorably with other existing methods.