There are several methods of handling missing data in a non-likelihood framework, imputation and the inverse probability weighting method being the two main approaches. These methods require auxiliary mod- els, namely the probability of observation for the inverse probabil- ity and the conditional distribution of missing data and their correct specification. Wang and Wang (2001) proposed a kernel method for these auxiliary models and investigated the relationship among various kernel-assisted methods and showed some asymptotic equivalence. In this paper we delve into some questions arisen from Wang and Wang (2001). We first derive an improved imputation method which subtracts the projection of the original imputation score onto the nuisance tangent space. Further, we look into the asymptotic behavior of our method and do a comparison with those described in Wang and Wang (2001). Our results are in contrast with those of Wang and Wang (2001) in that the projection from the improved imputation method becomes negligible when the conditional expectation is estimated. It turns out that under the conditions where our projection becomes negligible, the projection from the inverse probability estimating function is of nonnegligible order.
Keywords: kernel estimator, Imputation methods, Improved imputation methods, Semiparametric methods
Statistical Methodology | Statistical Theory
Zhang, Hui and Paik, Myunghee Cho, "An Improved Kernel Assisted Imputation Method in Missing Covariate Regression" (April 2007). Columbia University Biostatistics Technical Report Series. Working Paper 12.