Laws of large numbers and nearest neighbor distances

M D Penrose; J E Yukich

doi:10.1007/978-3-7908-2628-9_13

Laws of large numbers and nearest neighbor distances

M D Penrose, J E Yukich

Research output: Chapter or section in a book/report/conference proceeding › Book chapter

18 Citations (SciVal)

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
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	https://doi.org/10.1007/978-3-7908-2628-9_13
Publication status	Published - 2011

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

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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.",

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AU - Yukich, J E

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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.

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M3 - Book chapter

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BT - Advances in Directional and Linear Statistics:

A2 - Wells , Martin T

A2 - SenGupta , Ashis

PB - Physica-Verlag HD

CY - Berlin

ER -

Laws of large numbers and nearest neighbor distances

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