On high‐dimensional variance estimation in survey sampling

Using predictive modeling at different survey stages can improve the accuracy of a point estimator or help tackle issues such as missing values. So far, the existing literature on predictive models for survey data has predominantly concentrated on scenarios with low‐dimensional data, wherein the number of variables is small compared with the sample size. In this article, assuming a linear regression model, we show that customary variance estimators based on a first Taylor expansion or jackknife may suffer from substantial bias in a high‐dimensional setting. We explain why this is so through a mix of theoretical and empirical investigations. We propose some bias‐adjusted variance estimators and show, theoretically and empirically, that the proposed variance estimators perform well in terms of bias, even in a high‐dimensional setting.