The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. D. Evans, A. J. Jones. A proof of the gamma test. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 458 (2002), no. 2027, 2759--2799. MR1942807 (2003i:62081)
  2. D. Evans, A. J. Jones, W. M. Schmidt. Asymptotic moments of near-neighbour distance distributions. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 458 (2002), no. 2028, 2839--2849. MR1987515 (2004c:60027)
  3. J. Hansen. Theory of Simple Liquids. Academic Press, 2006. ISBN: 0-12-370535-5.
  4. M. Kohler, A. Krzyżak, H. Walk. Rates of convergence for partitioning and nearest neighbor regression estimates with unbounded data. J. Multivariate Anal. 97 (2006), no. 2, 311--323. MR2234025 (2009a:62169)
  5. L. F. Kozachenko, N. N. Leonenko. Sample estimate of entropy of a random vector. Problems of Information Transmission 23 (1987), no. 2, 9--16. MR0908626(88k:62067)
  6. N. Leonenko, L. Pronzato. Correction: A class of Rényi information estimators for multidimensional densities [ MR2458183]. Ann. Statist. 38 (2010), no. 6, 3837--3838. MR2766870 (2011k:94069)
  7. N. Leonenko, L. Pronzato, V. Savani. A class of Rényi information estimators for multidimensional densities. Ann. Statist. 36 (2008), no. 5, 2153--2182. MR2458183 (2010c:94013)
  8. E. Liitiäinen, A. Lendasse, F. Corona. A boundary corrected expansion of the moments of nearest neighbor distributions. Random Structures Algorithms 37 (2010), no. 2, 223--247. MR2676030(2011f:60026)
  9. E. Liitiäinen, A. Lendasse, F. Corona. On the statistical estimation of Rényi entropies. IEEE Conference on Machine Learning for Signal Processing (2009).
  10. M. Penrose. Random geometric graphs. Oxford Studies in Probability, 5. Oxford University Press, Oxford, 2003. xiv+330 pp. ISBN: 0-19-850626-0 MR1986198 (2005j:60003)
  11. M. D. Penrose. Laws of large numbers in stochastic geometry with statistical applications. Bernoulli 13 (2007), no. 4, 1124--1150. MR2364229 (2009b:60039)
  12. M. D. Penrose, J. E. Yukich. Laws of large numbers and nearest neighbor distances. Advances in directional and linear statistics, 189--199, Physica-Verlag/Springer, Heidelberg, 2011. MR2767541
  13. B. Ranneby, S. R. Jammalamadaka, A. Teterukovskiy. The maximum spacing estimation for multivariate observations. J. Statist. Plann. Inference 129 (2005), no. 1-2, 427--446. MR2126858 (2005k:62148)
  14. A. R. Wade. Explicit laws of large numbers for random nearest-neighbour-type graphs. Adv. in Appl. Probab. 39 (2007), no. 2, 326--342. MR2341576 (2008h:60044)
  15. J. E. Yukich. Probability theory of classical Euclidean optimization problems. Lecture Notes in Mathematics, 1675. Springer-Verlag, Berlin, 1998. x+152 pp. ISBN: 3-540-63666-8 MR1632875 (2000d:60018)
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.