### Abstract

Original language | English |
---|---|

Title of host publication | Advances in Directional and Linear Statistics: |

Subtitle of host publication | A Festschrift for Sreenivasa Rao Jammalamadaka |

Editors | Martin T Wells , Ashis SenGupta |

Place of Publication | Berlin |

Publisher | Physica-Verlag HD |

Pages | 189-199 |

ISBN (Electronic) | 9783790826289 |

ISBN (Print) | 9783790826272 |

DOIs | |

Publication status | Published - 2011 |

### Fingerprint

### Cite this

*Advances in Directional and Linear Statistics: A Festschrift for Sreenivasa Rao Jammalamadaka*(pp. 189-199). Berlin: Physica-Verlag HD . https://doi.org/10.1007/978-3-7908-2628-9_13

**Laws of large numbers and nearest neighbor distances.** / Penrose, M D; Yukich, J E.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Advances in Directional and Linear Statistics: A Festschrift for Sreenivasa Rao Jammalamadaka.*Physica-Verlag HD , Berlin, pp. 189-199. https://doi.org/10.1007/978-3-7908-2628-9_13

}

TY - CHAP

T1 - Laws of large numbers and nearest neighbor distances

AU - Penrose, M D

AU - Yukich, J E

PY - 2011

Y1 - 2011

N2 - We consider the sum of power weighted nearest neighbor distances in a sample of size n from a multivariate density f of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for large n, correcting some inaccuracies in the literature on the way. Motivation comes partly from the problem of consistent estimation of certain entropies of f.

AB - We consider the sum of power weighted nearest neighbor distances in a sample of size n from a multivariate density f of possibly unbounded support. We give various criteria guaranteeing that this sum satisfies a law of large numbers for large n, correcting some inaccuracies in the literature on the way. Motivation comes partly from the problem of consistent estimation of certain entropies of f.

UR - http://dx.doi.org/10.1007/978-3-7908-2628-9_13

U2 - 10.1007/978-3-7908-2628-9_13

DO - 10.1007/978-3-7908-2628-9_13

M3 - Chapter

SN - 9783790826272

SP - 189

EP - 199

BT - Advances in Directional and Linear Statistics:

A2 - Wells , Martin T

A2 - SenGupta , Ashis

PB - Physica-Verlag HD

CY - Berlin

ER -