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

Abstract

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.

Keywords:

• Design consistency
• elastic net
• Lasso
• random forest
• ridge regression
• XGBoost

Acknowledgments

We thank the Editor, an Associate Editor, and two referees for their comments and suggestions, which helped improving the paper substantially. We are very grateful to Professor Patrick Tardivel from the Université de Bourgogne for enlightening discussions about the lasso method.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The data are available on request at: https://www.ucd.ie/issda/data/commissionforenergyregulationcer/.

Additional information

Funding

The work of Mehdi Dagdoug was supported by grants of the Franche-Comté region and Médiamétrie. The work of David Haziza was supported by a grant of the Natural Sciences and Engineering Research Council of Canada.