Survey model-assisted estimation with the lasso
In survey statistics, the design-based Horvitz-Thompson estimator is a commonly used method of estimation. However, large amounts of auxiliary data are often available and can augment the survey data. Model-assisted regression estimators use this auxiliary data to fit regression models, which can improve the estimation of population quantities. In this paper we focus on the lasso model, proposed by Tibshirani (1996), and present several lasso-based regression estimators. A logistic lasso regression estimator is used for estimating a population proportion. In order to study the behavior of the lasso under various constraints, we ran simulations which assess the efficiency of the lasso-based estimators compared to other survey estimators. We then applied the estimators to Colorado forestry data.
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