An improved estimator for models with randomly missing data

Abstract

In the context of estimating θ from the density f(y|x,z,θ), relating responses y to covariates x and z, suppose that observations on y and z are available for the total sample but observations on x are available only for a random subsample of the total sample, termed the validation sample. We consider a generalized method of moment estimator for θ from such data, which is nonparametric with respect to the density relating x to z, f(x|z). The estimator relies on estimating the densityf(y|z,θ) relatingy toz from the validation sample. It is shown that the estimator is √N consistent, asymptotically normal, and more efficient than other existing estimators. An easily computable covariance matrix is also provided.

Keywords:

• Missing at random
• missing data
• kernel estimation