English

Refined Pinsker's and reverse Pinsker's inequalities for probability distributions of different dimensions

Statistics Theory 2022-11-03 v3 Probability Statistics Theory

Abstract

We provide optimal lower and upper bounds for the augmented Kullback-Leibler divergence in terms of the augmented total variation distance between two probability measures defined on two Euclidean spaces having different dimensions. We call them refined Pinsker's and reverse Pinsker's inequalities, respectively.

Keywords

Cite

@article{arxiv.2203.00500,
  title  = {Refined Pinsker's and reverse Pinsker's inequalities for probability distributions of different dimensions},
  author = {Michele Caprio},
  journal= {arXiv preprint arXiv:2203.00500},
  year   = {2022}
}