If you need an accessible version of this item please contact JSTOR User Support

Feasibility of Multivariate Density Estimates

David W. Scott and M. P. Wand
Biometrika
Vol. 78, No. 1 (Mar., 1991), pp. 197-205
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2336910
Stable URL: http://www.jstor.org/stable/2336910
Page Count: 9
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
Feasibility of Multivariate Density Estimates
Preview not available

Abstract

The `curse of dimensionality' has been interpreted as suggesting that kernel methods have limited applicability in more than several dimensions. In this note, qualitative and quantitative performance measures for multivariate density estimates are examined. Optimal pointwise and global window widths for mean absolute and mean squared errors are compared for multivariate data. One result is that the optimal pointwise absolute and squared error window widths are nearly equal for all dimensions. We also show that sample size requirements predicted by absolute rather than squared error criterion are substantially less. Further reductions are realized by using a coefficient of variation criterion. Finally, an example of a 10-dimensional kernel density estimate is given. It is suggested that the true nature of the curse of dimensionality is as much the lack of full rank as sparseness of the data.

Page Thumbnails

  • Thumbnail: Page 
[197]
    [197]
  • Thumbnail: Page 
198
    198
  • Thumbnail: Page 
199
    199
  • Thumbnail: Page 
200
    200
  • Thumbnail: Page 
201
    201
  • Thumbnail: Page 
202
    202
  • Thumbnail: Page 
203
    203
  • Thumbnail: Page 
204
    204
  • Thumbnail: Page 
205
    205