Lower Bounds for the Total Variation Distance Given Means and Variances of Distributions
Tomohiro Nishiyama
TL;DR
This paper establishes lower bounds on the total variation distance between two probability measures based on their means and variances, providing a tight bound in the one-dimensional case.
Contribution
It introduces new lower bounds for total variation distance given means and variances, including a tight bound for the one-dimensional scenario.
Findings
Derived lower bounds for total variation distance given means and variances.
Established a tight bound for the one-dimensional case.
Applicable to arbitrary probability measures on real d-space.
Abstract
For arbitrary two probability measures on real d-space with given means and variances (covariance matrices), we provide lower bounds for their total variation distance. In the one-dimensional case, a tight bound is given.
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Taxonomy
TopicsStatistical Methods and Inference · Advanced Statistical Methods and Models · Bayesian Modeling and Causal Inference