Model-Assisted Estimation Through Random Forests in Finite Population Sampling

Abstract

In surveys, the interest lies in estimating finite population parameters such as population totals and means. In most surveys, some auxiliary information is available at the estimation stage. This information may be incorporated in the estimation procedures to increase their precision. In this article, we use random forests (RFs) to estimate the functional relationship between the survey variable and the auxiliary variables. In recent years, RFs have become attractive as National Statistical Offices have now access to a variety of data sources, potentially exhibiting a large number of observations on a large number of variables. We establish the theoretical properties of model-assisted procedures based on RFs and derive corresponding variance estimators. A model-calibration procedure for handling multiple survey variables is also discussed. The results of a simulation study suggest that the proposed point and estimation procedures perform well in terms of bias, efficiency and coverage of normal-based confidence intervals, in a wide variety of settings. Finally, we apply the proposed methods using data on radio audiences collected by Médiamétrie, a French audience company. Supplementary materials for this article are available online.