Model-assisted estimation in high-dimensional settings for survey data

Model-assisted estimators have attracted a lot of attention in the last three decades. These estimators attempt to make an efficient use of auxiliary information available at the estimation stage. A working model linking the survey variable to the auxiliary variables is specified and fitted on the sample data to obtain a set of predictions, which are then incorporated in the estimation procedures. A nice feature of model-assisted procedures is that they maintain important design properties such as consistency and asymptotic unbiasedness irrespective of whether or not the working model is correctly specified. In this article, we examine several model-assisted estimators from a design-based point of view and in a high-dimensional setting, including linear regression and penalized estimators. We conduct an extensive simulation study using data from the Irish Commission for Energy Regulation Smart Metering Project, to assess the performance of several model-assisted estimators in terms of bias and efficiency in this high-dimensional data set.