Debiased machine learning for combining probability and non-probability survey data

TL;DR

This paper develops a framework for using machine learning in double robust estimators to accurately estimate population means from combined probability and non-probability survey data, even with model misspecification.

Contribution

It introduces a general approach allowing valid use of machine learning for nuisance estimation in double robust estimators with complex survey designs.

Findings

DR estimators are asymptotically normal with machine learning nuisance estimates

Cross-fitting improves estimator validity under model misspecification

Simulation shows superior performance over parametric models

Abstract

We consider the problem of estimating the finite population mean $\bar{Y}$ of an outcome variable $Y$ using data from a nonprobability sample and auxiliary information from a probability sample. Existing double robust (DR) estimators of this mean $\bar{Y}$ require the estimation of two nuisance functions: the conditional probability of selection into the nonprobability sample given covariates $X$ that are observed in both samples, and the conditional expectation of $Y$ given $X$. These nuisance functions can be estimated using parametric models, but the resulting estimator of $\bar{Y}$ will typically be biased if both parametric models are misspecified. It would therefore be advantageous to be able to use more flexible data-adaptive / machine-learning estimators of the nuisance functions. Here, we develop a general framework for the valid use of DR estimators of $\bar{Y}$ when the design of the probability sample uses sampling without replacement at the first stage and data-adaptive / machine-learning estimators are used for the nuisance functions. We prove that several DR estimators of $\bar{Y}$, including targeted maximum likelihood estimators, are asymptotically normally distributed when the estimators of the nuisance functions converge faster than the $n^{1/4}$ rate and cross-fitting is used. We present a simulation study that demonstrates good performance of these DR estimators compared to the corresponding DR estimators that rely on at least one correctly specified parametric model.