Survey Statistics: double-plus robustness

Meng (2022) pops up a lot here: “it is the people” (the launch of this blog series a year ago !), “probability samples vs epsem samples vs SRS samples”, “divine probabilities”, and last week’s “GREG”. Like a lot of Meng’s papers, it deserves several rereads. Let’s zoom in on the part about the Generalized REGression estimator (that doesn’t specifically say “GREG”). Green anotations are mine: Meng (2022)‘s (5.2) is the first way of writing GREG in our post “GREG”, from Särndal, Swensson, Wretman (1992): That book goes on to say that GREG often takes a super simple form: Meng (2022) doesn’t mention this as far as I can tell ? Although I think Meng’s example satisfies the conditions the book Särndal, Swensson, Wretman (1992) goes on to describe: the regression model assumes constant variance and has an intercept. Anyways, back to the title of this post. Meng emphasizes that GREG is not only “double robust” (consistent if either the outcome model or response model are correct), but…