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In this talk, I will discuss two methods -- universal inference and the HulC -- which use sample-splitting to construct confidence sets which are valid under very weak regularity conditions. Universal inference uses sample-splitting to ease the construction of likelihood-ratio based confidence sets. The HulC uses sample-splitting to significantly weaken the regularity conditions needed for the validity of classical resampling based methods (the bootstrap and sub-sampling). These methods are easy to apply, yield valid inference in a wide-range of challenging problems, and achieve these strong guarantees at a surprisingly small statistical price.

The two main papers I will discuss are:

https://arxiv.org/abs/1912.11436 (universal inference)
https://arxiv.org/abs/2105.14577 (the HulC)

This is based on joint work with Arun Kuchibhotla, Aaditya Ramdas and Larry Wasserman.