Skip Navigation

Biometrika 1987 74(4):751-762; doi:10.1093/biomet/74.4.751
© 1987 by Biometrika Trust
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by HALL, P.
Right arrow Articles by CABRERA, J.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Kernel density estimation with spherical data

PETER HALL, G. S. WATSON and JAVIER CABRERA

Department of Statistics, Australian National University Canberra, ACT 2601, Australia
Fine Hall, Princeton University Princeton, New Jersey 08544, U.S.A.
Department of Statistics, Rutgers University New Brunswick, New Jersey 08903, U.S.A.

We study two natural classes of kernel density estimators for use with spherical data. Members of both classes have already been used in practice. The classes have an element in common, but for the most part they are disjoint. However, all members of the first class are asymptotically equivalent to one another, and to a single element of the second class. In this sense the second class ‘contains’ the first. It includes some estimators which out-perform all those in the first class, if loss is measured in either squared-error or Kullback—Leibler senses. Explicit formulae are given for bias, variance and loss, and large-sample properties of these quantities are described. Numerical illustrations are presented.

Key Words: Bias • Cross-validation • Kernel density estimation • Loss • Spherical data • Variance


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.