Comments on “Statistical inference with non-probability survey samples”
Section 1. Introduction

Thanks to Dr. Changbao Wu for an excellent review of the previous work and open issues for statistical inference from non-probability samples. Given the large and rapidly developing work in this area, Dr. Wu was understandably unable to cover all of it; my own understanding has blinders as well but I will touch on a few additional approaches that relate to topics he considered. I will also discuss the issue of modeling versus weighting for different inferential targets, and use his discussion and conclusions to highlight the critical importance of probability samples MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaqcLbwaqa aaaaaaaaWdbiaa=nbiaaa@37A3@  in particular high-quality studies that focus on estimation of relevant covariates MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaqcLbwaqa aaaaaaaaWdbiaa=nbiaaa@37A3@  to improve inference for the profusion of non-probability samples used as replacements for traditional probability samples in many research and official statistics settings. To avoid notation confusion, all notation will follow that of Wu, except where new notation is required.

Section 2 reviews additional approaches to combining data from probability and non-probability surveys. Section 3 briefly reviews the issue of weighting versus modeling when adjusting non-probability survey data. Section 4 reviews some recent developments in sensitivity analyses of standard assumptions for adjusting non-probability survey data using probability survey data. Section 5 concludes with call to systematically design a set of probability surveys with the explicit purpose of adjusting non-probability surveys.


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