A method to find an efficient and robust sampling strategy under model uncertainty

TL;DR

This paper introduces a new sampling strategy selection method that accounts for model uncertainty, improving robustness and efficiency over traditional approaches, demonstrated through real data analysis.

Contribution

It proposes a risk-based approach for choosing sampling designs under model uncertainty, enhancing robustness compared to standard methods.

Findings

The new method outperforms traditional probability proportional-to-size sampling under model misspecification.

It effectively balances efficiency and robustness in sampling design decisions.

Real data application confirms the practical benefits of the proposed approach.

Abstract

We consider the problem of deciding on sampling strategy, in particular sampling design. We propose a risk measure, whose minimizing value guides the choice. The method makes use of a superpopulation model and takes into account uncertainty about its parameters. The method is illustrated with a real dataset, yielding satisfactory results. As a baseline, we use the strategy that couples probability proportional-to-size sampling with the difference estimator, as it is known to be optimal when the superpopulation model is fully known. We show that, even under moderate misspecifications of the model, this strategy is not robust and can be outperformed by some alternatives