Abstract
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.
Original language | English |
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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 |