Statistical Inference for Imputed Estimators Based on Regularized Imputation in Surveys

Abstract

Penalized regression serves as a powerful alternative to ordinary least squares for handling multicollinearity. This property also holds true in survey sampling settings, where penalized regression is implemented for data imputation. In this paper, we analyze the behaviour of penalized regression estimators in survey contexts, focusing primarily on ridge regression and its debiased versions based on minimizing the conditional mean squared error (CMSE). Our study demonstrates that the proposed debiased approach performs well in controlling bias across various correlation structures and covariate dimensions, although it does not strictly outperform standard penalty selection methods such as cross-validation. Furthermore, we evaluate two methods for estimating the MSE of the imputed estimator: one based on Särndal's variance estimation framework and another relying on a pseudo-population bootstrap. The study of these MSE estimators illustrates how high-dimensional data impacts the validity and stability of these MSE estimators.