Statistics and Its Interface

Volume 6 (2013)

Number 3

Imputation methods for quantile estimation under missing at random

Pages: 369 – 377



Shu Yang (Department of Statistics, Iowa State University, Ames, Iowa, U.S.A.)

Jae-Kwang Kim (Department of Statistics, Iowa State University, Ames, Iowa, U.S.A.)

Dong Wan Shin (Department of Statistics, Ewha University, Seoul, Korea)


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.


Bahadur representation, estimating equation, fractional hot deck imputation, jackknife variance estimator, linearization method, nonparametric imputation, Woodruff variance

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