Year: 2025
Type: preprint
Abstract: We consider estimation of the finite population mean $\bar{Y}$ of an outcome $Y$ using data from a nonprobability sample and auxiliary information from a probability sample. Existing double robust (DR) estimators of this mean $\bar{Y}$ require 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 models are misspecified. It would therefore be advantageous to be able to use more flexible data-adaptive / machine-learning estimators of the nuisance functions. 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, and describe an application to sexual and reproductive health survey data.
Source: arXiv (Cornell University)
Author: Seaman, Shaun
Institutions: University of Cambridge, MRC Biostatistics Unit
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Wellcome Trust
OpenAlex ID: W4416867504
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