For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are refined for random variables with finite second moment.
Bibliographical noteFunding Information:
This research was partially supported by NSF grant DMS-1612961 , the Humboldt Foundation and SFB 701 at Bielefeld University .
- Cramer's theorem
- Normal characterization
- Stability problems