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.

Weighting procedures are commonly applied in surveys to compensate for nonsampling errors such as nonresponse errors and coverage errors. Two types of weight-adjustment procedures are commonly used in the context of unit nonresponse: (i) nonresponse propensity weighting followed by calibration, also known as the two-step approach and (ii) nonresponse calibration weighting, also known as the one-step approach. In this article, we discuss both approaches and warn against the potential pitfalls of the one-step procedure. Results from a simulation study, evaluating the properties of several point estimators, are presented.

Sinha & Rao (2009) proposed estimation procedures designed for small-area means, based on robustified maximum likelihood estimators and robust empirical best linear unbiased predictors. Their methods are of the plug-in type and may be biased. Bias-corrected estimators have been proposed by Chambers et al. (2013). Here, we investigate two new approaches: one relying on the work of Chambers (1986), and the second using the concept of conditional bias to measure the influence of units in the population. These two classes of estimators also include correction terms for the bias but are both fully bias-corrected, in the sense that the corrections account for the potential impact of the other domains on the small area of interest. Monte Carlo simulations suggest that the Sinha–Rao method and the bias-adjusted estimator of Chambers et al. (2013) may exhibit a large bias, while the new procedures often offer lower bias and mean squared error. A parametric bootstrap procedure is considered for constructing confidence intervals.

Item nonresponse in surveys is often treated through some form of imputation. We introduce multiply robust imputation in finite population sampling. This is closely related to multiple robustness, which extends double robustness. In practice, multiple nonresponse models and multiple imputation models may be fitted, each involving different subsets of covariates and possibly different link functions. An imputation procedure is said to be multiply robust if the resulting estimator is consistent when all models but one are misspecified. A jackknife variance estimator is proposed and shown to be consistent. Random and fractional imputation procedures are discussed. A simulation study suggests that the proposed estimation procedures have low bias and high efficiency.