Bandwidth selection for kernel density estimators of multivariate level sets and highest density regions

Understand

We consider bandwidth matrix selection for kernel density estimators (KDEs) of density level sets in $\mathbb{R}^d$, $d \ge 2$.

• We also consider estimation of highest density regions, which differs from estimating level sets in that one specifies the probability content of the set rather than specifying the level directly.
• This complicates the problem.
• Bandwidth selection for KDEs is well studied, but the goal of most methods is to minimize a global loss function for the density or its derivatives.