## Abstract

We consider bandwidth matrix selection for kernel density estimators of density level sets in ℝ ^{d} , ≥ 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. The loss we consider here is instead the measure of the symmetric difference of the true set and estimated set. We derive an asymptotic approximation to the corresponding risk. The approximation depends on unknown quantities which can be estimated, and the approximation can then be minimized to yield a choice of bandwidth, which we show in simulations performs well. We provide an R package lsbs for implementing our procedure.

Original language | English (US) |
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Pages (from-to) | 4313-4376 |

Number of pages | 64 |

Journal | Electronic Journal of Statistics |

Volume | 12 |

Issue number | 2 |

DOIs | |

State | Published - 2018 |

### Bibliographical note

Funding Information:∗Supported in part by NSF Grant DMS-1712664 †Supported in part by a University of Minnesota Grant-in-Aid grant

Publisher Copyright:

© 2018, Institute of Mathematical Statistics. All rights reserved.

## Keywords

- Bandwidth selection
- Highest density region estimation
- Kernel density estimator
- Level set estimation