Using missing data methods to correct for measurement error in a distribution function

Abstract

This paper considers the use of imputation and weighting to correct for measurement error in the estimation of a distribution function. The paper is motivated by the problem of estimating the distribution of hourly pay in the United Kingdom, using data from the Labour Force Survey. Errors in measurement lead to bias and the aim is to use auxiliary data, measured accurately for a subsample, to correct for this bias. Alternative point estimators are considered, based upon a variety of imputation and weighting approaches, including fractional imputation, nearest neighbour imputation, predictive mean matching and propensity score weighting. Properties of these point estimators are then compared both theoretically and by simulation. A fractional predictive mean matching imputation approach is advocated. It performs similarly to propensity score weighting, but displays slight advantages of robustness and efficiency