Fractional imputation using regression imputation model

@inproceedings{Kim2002FractionalIU,
  title={Fractional imputation using regression imputation model},
  author={Jae Kwang Kim},
  year={2002}
}
Consider a finite population of N elements identified by a set of indices U = {1, 2, ..., N}. Associated with each unit i in the population there is a study variable yi and a vector xi of auxiliary variables. Let A denote the set of indices for the elements in a sample selected by a set of probability rules called the sampling mechanism. Let the population quantity of interest be θN = ∑N i=1 yi or θN = N −1 ∑N i=1 yi and let θ̂n be a linear estimator of θN based on the full sample, θ̂n = ∑ 

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