Paul, I don't quite follow. You're asking would a standard error estimate be consistent estimator of a point estimate?
My first reaction is that, definitionally, I don't think a standard error can be a consistent estimator of anything. Consistency is an asymptotic property, but SE depends inversely on N. So asymptotically, as N approaches infinity, SE always approaches a limit of 0, regardless of any other details about the situation. A related question might be, when would the complete-case estimate of the SE be an *unbiased* estimate of the (unobserved) SE for the dropped cases? If that's what you want, then I'm pretty sure the answer would be: (a) under MCAR and (b) with a 50% deletion rate. If (a) is violated, you're in uncharted waters. You know your complete-case sample is not representative of the population from which the dropped cases are drawn. If (b) is violated, the SEs between the retained and dropped cases will differ because they are based on different Ns. Let me know if I've misread. Pat On Mon, May 8, 2023 at 3:16 PM Paul Von hippel <[email protected]> wrote: > Hi, all. What is known about the properties of standard error estimates > obtained using listwise deletion. When are they consistent estimates of the > listwise deleted point estimates? > > -- > > > Thanks! > Paul von Hippel > Professor, Associate Dean for Research > LBJ School of Public Affairs > University of Texas, Austin > > > -- He/him/his
