Design-Unbiased Statistical Learning in Survey Sampling

Abstract

Design-consistent model-assisted estimation has become the standard practice in survey sampling. However, design consistency remains to be established for many machine-learning techniques that can potentially be very powerful assisting models. We propose a subsampling Rao-Blackwell method, and develop a statistical learning theory for exactly design-unbiased estimation with the help of linear or non-linear prediction models. Our approach makes use of classic ideas from Statistical Science as well as the rapidly growing field of Machine Learning. Provided rich auxiliary information, it can yield considerable efficiency gains over standard linear model-assisted methods, while ensuring valid estimation for the given target population, which is robust against potential mis-specifications of the assisting model, even if the design consistency of following the standard recipe for plug-in model-assisted estimator cannot be established.

Robust quasi‐randomization‐based estimation with ensemble learning for missing data

“…However, $$$ {\hat{\theta}}^{(1)} $$$ is only based on one random split of $$$ {s}_r={s}_1\cup {s}_2 $$$, which leads to additional variance due to learning from $$$ {s}_1 $$$ instead of $$$ {s}_r $$$. As proposed by Sanguiao‐Sande and Zhang (2021), we can reduce the variance of $$$ {\hat{\theta}}^{(1)} $$$ by applying the Monte Carlo Rao–Blackwell (RB) method. Then, our proposed estimator is given by $$$$ {\hat{\theta}}_{\mathrm{SRB}}=\frac{1}{K}\sum \limits_{k=1}^K{\hat{\theta}}^{(k)},\kern0.5em $$$$ where $$$ {\hat{\theta}}^{(k)} $$$ is the estimator () calculated from the k th Monte Carlo subsamples, $$$ \left({s}_1^{(k)},{s}_2^{(k)}\right) $$$ such that …”

“…It is similar in spirit to the super learner proposed by Van der Laan et al (2007), which aims to improve prediction by creating a weighted combination of many candidate outcome learners, but in a different manner to ours. While our use of the cell response model is a robust extension of the randomization‐based approach of unbiased statistical learning proposed by Sanguiao‐Sande and Zhang (2021), which applies a single assisting outcome model to the complete sample observations by the subsampling Rao–Blackwell method.…”