Self-normalizing concentration inequality for Neyman’s variance estimator

Derive a self-normalizing concentration inequality involving Neyman’s variance estimator for completely randomized experiments, analogous to the self-normalizing concentration result obtained for independent treatment assignments.

Background

For completely randomized experiments, the paper constructs empirical Bernstein and Bennett confidence intervals by first establishing a separate concentration inequality for Neyman’s variance estimator and then combining it with an oracle Bernstein inequality through a union bound. This differs from the independent-assignment setting, where a self-normalizing construction directly yields a concentration inequality involving an empirical variance quantity.

The authors explicitly state that they were unable to derive such a self-normalizing result for completely randomized experiments. Developing one could replace the two-step union-bound argument and potentially yield sharper non-asymptotic confidence intervals for the sample average treatment effect.