Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T22:30:04.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Tests of Randomness Based on the K-NN Distances for Data from a Bounded Region

Published online by Cambridge University Press:  27 July 2009

Renata Rotondi
Renata Rotondi
Affiliation:
C.N.R.-Istituto per le Applicazioni della Matematica e dell'InformaticaVia Ampère, 56, 20131 Milano, Italy
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes some new statistics based on k-NN distances for assessing the uniformity of a set of points belonging to a d-dimensional bounded region. Size and power of the tests have been estimated and compared to those of the modified Hopkins' statistic.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 4 , October 1993 , pp. 557 - 569
Copyright
Copyright © Cambridge University Press 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Abramowitz, M. & Stegun, I.A. (1972). Handbook of mathematical functions. New York: Dover Publications.Google Scholar
2.Bentley, J.L. (1980). Multidimensional divide-and-conquer. ACM Communication 23(4): 214–229.CrossRefGoogle Scholar
3.Byth, K. & Ripley, B.D. (1980). On sampling spatial patterns by distance methods. Biometrics 36: 279–284.Google Scholar
4.Clark, P.J. & Evans, F.C. (1954). Distance to nearest neighbour as a measure of spatial pattern in biological populations. Ecology 35: 445–453.CrossRefGoogle Scholar
5.Cressie, N.A.C. (1991). Statistics for spatial data. New York: John Wiley.Google Scholar
6.Diggle, P.J. (1983). Statistical analysis of spatial point patterns. New York: Academic Press.Google Scholar
7.Friedman, J.H., Baskett, F., & Shustek, L.J. (1975). An algorithm for finding nearest neighbours. IEEE Transactions on Computers C-24: 1000–1006.Google Scholar
8.Fukunaga, K. & Narendra, P.M. (1975). A branch and bound algorithm for computing k-nearest neighbours. IEEE Transactions on Computers C-24: 750–753.CrossRefGoogle Scholar
9.Holgate, P. (1965). Some new tests of randomness. Journal of Ecology 53: 261–266.CrossRefGoogle Scholar
10.Hopkins, B. (1954). A new method of determining the type of distribution of plant individuals. Annals of Botany 18: 213–226.CrossRefGoogle Scholar
11.Kirkpatrick, D. (1983). Optimal search in planar subdivisions. SIAM Journal on Computing 12: 28–35.CrossRefGoogle Scholar
12.Kittler, J. (1978). A method for determining k-nearest neighbours. Kybernetes 7: 313–315.CrossRefGoogle Scholar
13.Lewis, T.G. & Payne, W.H. (1973). Generalized feedback shift register pseudorandom number algorithm. Journal of the Association for Computing Machinery 20(3): 456–468.CrossRefGoogle Scholar
14.Murtagh, F. (1984). A review of fast techniques for nearest neighbour searching. Compstat 6: 143–147.Google Scholar
15.Richetin, M., Rives, G., & Naranjo, M. (1980). Algorithme rapide pour la determination des k plus proches voisins. RAIRO Informatique/Computer Science 14(4): 369–378.Google Scholar
16.Ripley, B.D. (1977). Modelling spatial patterns. Journal of the Royal Statistical Society: Series B 39:172–192.Google Scholar
17.Ripley, B.D. (1979). Tests of randomness for spatial point patterns. Journal of the Royal Statistical Society: Series B 41(3): 368–374.Google Scholar
18.Ripley, B.D. (1981). Spatial statistics. New York: John Wiley.Google Scholar
19.Ripley, B.D. (1988). Statistical inference for spatial processes. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
20.Rotondi, R. (1988). Test di casualità per dati multidimensionali da regioni di campionamento limitate. Atti del XII Convegno AMASES, Palermo (1), 14–16 09, pp. 683–702.Google Scholar
21.Thompson, H.R. (1956). Distribution of distance to n-th nearest neighbour in a population of randomly distributed individuals. Ecology 37: 391–394.CrossRefGoogle Scholar
22.Wilks, S.S. (1962). Mathematical statistics. New York: John Wiley.Google Scholar
23.Yuval, G. (1976). Finding near neighbours in k-dimensional space. Information Processing Letters 3(4): 113–114.CrossRefGoogle Scholar
24.Yuval, G. (1976). Finding nearest neighbours. Information Processing Letters 5(3): 63–65.CrossRefGoogle Scholar
25.Zeng, G. & Dubes, R.C. (1985). A comparison of tests for randomness. Pattern Recognition 18(2): 191–198.Google Scholar
26.Zeng, G. & Dubes, R.C. (1985). A test for spatial randomness based on k-NN distances. Pattern Recognition Letters 3: 85–91.CrossRefGoogle Scholar