Campus Units

Statistics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

4-2020

Journal or Book Title

Journal of the Royal Statistical Society: Series B

Volume

82

Issue

2

First Page

445

Last Page

465

DOI

10.1111/rssb.12354

Abstract

Non-probability samples become increasingly popular in survey statistics but may suffer from selection biases that limit the generalizability of results to the target population. We consider integrating a non-probability sample with a probability sample which provides high-dimensional representative covariate information of the target population. We propose a two-step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded-concave penalties to select important variables for the sampling score of selection into the non-probability sample and the outcome model. We show that the penalized estimating equation approach enjoys the selection consistency property for general probability samples. The major technical hurdle is due to the possible dependence of the sample under the finite population framework. To overcome this challenge, we construct martingales which enable us to apply Bernstein concentration inequality for martingales. In the second step, we focus on a doubly robust estimator of the finite population mean and re-estimate the nuisance model parameters by minimizing the asymptotic squared bias of the doubly robust estimator. This estimating strategy mitigates the possible first-step selection error and renders the doubly robust estimator root-n consistent if either the sampling probability or the outcome model is correctly specified.

Comments

This is a manuscript of an article published as Yang, Shu, Jae Kwang Kim, and Rui Song. "Doubly robust inference when combining probability and non‐probability samples with high dimensional data." Journal of the Royal Statistical Society: Series B (Statistical Methodology) 82 (2020): 445-465. doi: 10.1111/rssb.12354. Posted with permission.

Copyright Owner

Royal Statistical Society

Language

en

File Format

application/pdf

Published Version

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