Abstract
In this article, we consider an imputation method to handle missing response values based on semiparametric quantile regression estimation. In the proposed method, the missing response values are generated using the semiparametrically estimated conditional quantile regression function at given values of covariates. Then the imputed values are used to estimate a parameter defined as the expected value of a function involving the response and covariate variables. We derive the asymptotic distribution of our estimator constructed with the imputed data and provide a variance estimator. In simulation, we compare our semiparametric quantile regression imputation method to fully parametric and nonparametric alternatives and evaluate the variance estimator based on the asymptotic distribution. We also discuss an extension for estimating a parameter defined through an estimation equation.
Highlights
Missing data is frequently encountered in many disciplines
Imputation provides a complete data set by replacing missing response variables with imputed values
In the presence of item nonresponse, imputation simplifies analyses because standard analytical tools can be applied to any imputed data set and the resulting point estimates are consistent across different users
Summary
Missing data is frequently encountered in many disciplines. If the variables that explain the missing data are related to the response of interest, an inference based on ignoring missing undermines efficiency and often leads to biases and misleading conclusions. Imputation provides a complete data set by replacing missing response variables with imputed values. In a recent work by Wang and Chen (2009), multiple imputed values are independently drawn from observed respondents with probabilities proportional to kernel distances between missing cells and donors. Both HDI and Wang and Chen (2009) are purely nonparametric, so the stability and accuracy of the estimators depend on the dimensionality and the sample size concerned.
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