Open florianhartig opened 5 years ago
Mea culpa, I have been wanting to write this paper for so long. Maybe this summer. I had some other people asking about it.
About other references: I think there are quite a bit more references that the unsuspecting eye suggests, although they might be scattered. I believe the integer randomisation procedure as such is sufficiently covered by Dunn and Smyth (1996). To simulate from the fitted model is known as the parametric bootstrap, and the recommendation to use this has popped up in various places over the years (Simon Wood who develops mgcv always recommended it, I seem to remember it was also mentioned in Gelman & Hill 2007). Moreover, Bayesians have used the same or similar procedures (alas, often with the Dunn & Smyth trick) for years, see discussion in https://esajournals.onlinelibrary.wiley.com/doi/10.1002/ecm.1314. The difference is obviously that they sample from the posterior instead of the MLE. There is some work / discussion to do about the exact distributional properties, as residuals won't be exactly uniform for biased estimators (e.g. REs).
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