Sums of Functions of Nearest Neighbor Distances, Moment Bounds, Limit Theorems and a Goodness of Fit Test.

Abstract

The limiting behavior of sums of functions of nearest neighbor distances is studied for an m dimensional sample. A central limit theorem and moment bounds for such sums, and an invariance principle for the empirical process of nearest neighbor distances are both established. As a consequence the asymptotic behavior of a practicable goodness of fit test is obtained based on nearest neighbor distances.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1982
Accession Number
ADA123902

Entities

People

  • Leo Breiman
  • Peter J. Bickel

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Cells
  • Convergence
  • Covariance
  • Data Science
  • Distribution Functions
  • Gaussian Processes
  • Goodness Of Fit Tests
  • Inequalities
  • Information Science
  • Invariance
  • Probability
  • Probability Distributions
  • Random Variables
  • Sequences
  • Statistics
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.