It is simply the Fisher information for a parametric location-shift model.
For people of interest, here is a final exam question from my measure theory course in 2023, showing that convolution always reduces the information.
Fang Han
273 posts
- Not a junior researcher fighting for the space of the Annals of Statistics any more… but hey, every acceptance still deserves a new “bound”.
- We prove that the Abadie-Imbens matching estimator is bootstrap consistent—as long as you scale up the number of matches.
On the consistency of bootstrap for matching estimators. arxiv.org/abs/2410.23525 - Wow, impressive!!! My morning attempt using martingale theory only...
I only knew one proof of the DKW inequality and it's not easy at all ! Nice achievement arxiv.org/abs/2403.16651 - Wow, what a day to start with: a new result for the old Erdos–Szekeres problem, from the best in the world!🤩 Some super elementary properties for the Erdos–Szekeres problem (i.e., determining the length of the longest increasing sequence of a uniform permutation):
Sourav Chatterjee, Persi Diaconis: A Vershik-Kerov theorem for wreath products arxiv.org/abs/2408.04364 arxiv.org/pdf/2408.04364 - My lecture notes on permutation processes
- We give the closed-form expression for the asymptotic variance of the Abadie-Imbens matching estimator.
Songliang Chen, Fang Han: On the limiting variance of matching estimators arxiv.org/abs/2411.05758 arxiv.org/pdf/2411.05758 - People own to know that all these concentration inequalities will automatically hold true, W.O. ANY assumption, if we change the sampling paradigm. Here is an example; a grand Talagrand inequality when the observations are sampled w.o. replacement from a finite pop:
- My favorite quote of Talagrand (Probability in Banach Spaces, with Ledoux). Talagrand has the magic to turn complex things simple.
The real challenge in VC type theorems, which is usually hidden in learning theory, is the measurability requirement on the studied objects. This is a long-forsaken bug that one you noticed, is hard to get away from. - This is a fun collaboration, for which I learnt a lot from two coauthors Peng (@pengding00) and Zhexiao (@zzzxlin). A special shout-out to Zhexiao, who just started his 2nd year PhD study (!).We revisit the Abadie-Imbens study on nearest neighbor matching and show that, with a diverging number of nearest neighbors, matching estimators can be doubly robust and semiparametrically efficient for estimating the average treatment effect econometricsociety.org/publications/e…
- Hmmm... 3 AoS papers in one issue; what should I say? congrats to myself 🤪? Random matrix theory: projecteuclid.org/euclid.aos/160… Rank correlation: projecteuclid.org/euclid.aos/160… Variance estimation: projecteuclid.org/euclid.aos/160…
- Rina, Peng (@pengding00), Nicole, and I are organizing an IMSI workshop aimed at forging connections between causal inference, distribution-free methods, and probability theory, within the overarching theme of "permutation".
