Quantile Estimation After Multiple Imputation

• Activity Number: 363
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Joerg Drechsler*+ and Robin Mitra
• Companies: Institute for Employment Research (IAB) and University of Southampton
• Keywords: multiple imputation ; quantile estimation ; parametric ; box-cox transformation

Abstract

When estimating quantiles of an unknown univariate distribution it is common to use the sample quantile as an unbiased point estimator for the true quantile and estimate its variance using some kind of resampling method, such as the bootstrap or the jack-knife. However, as we illustrate in this talk, using this strategy for a dataset for which missing observations have been multiply imputed will lead to conservative variance estimates based on Rubin's combining rules. The reason is that the sample quantile is not a self-efficient estimator as defined by Meng (1994). We propose a straightforward maximum likelihood estimator for the quantile using a box-cox transformation that allows valid inferences after multiple imputation if the assumptions of the box-cox transformation are met. We illustrate through simulation and real data applications that the estimator is more efficient than the estimator based on the sample quantile and unbiased given that the sample data can be approximated by a normal distribution after the box-cox transformation.