Wasserman on Spanos and Hennig on “Low Assumptions, High Dimensions” (2011)
(originating U-PHIL : “Deconstructing Larry Wasserman” by Mayo )
Thanks to Aris and others for comments .
Response to Aris Spanos:
1. You don’t prefer methods based on weak assumptions? Really? I suspect Aris is trying to be provocative. Yes such inferences can be less precise. Good. Accuracy is an illusion if it comes from assumptions, not from data.
2. I do not think I was promoting inferences based on “asymptotic grounds.” If I did, that was not my intent. I want finite sample, distribution free methods. As an example, consider the usual finite sample (order statistics based) confidence interval for the median. No regularity assumptions, no asymptotics, no approximations. What is there to object to?
3. Indeed, I do have to make some assumptions. For simplicity, and because it is often reasonable, I assumed iid in the paper (as I will here). Other than that, where am I making any untestable assumptions in the example of the median?
4. I gave a very terse and incomplete summary of Davies’ work. I urge readers to look at Davies’ papers; my summary does not do the work justice. He certainly did not advocate eyeballing the data. Continue reading