Nonparametric Discrimination and Density Estimation.
Abstract
The asymptotic properties of generalized nearest neighbor rules and other nonparametric discrimination rules are investigated. The problem is to estimate an M-ary valued parameter theta if an observed random vector X and data consisting of a sequence of independent random vectors (X sub 1, theta sub 1) (X sub n, theta sub n) with the same distrubition as (X, theta) are given. Conditions are given under which the rules are asymptotically optimal. Consistent density estimates can be used to construct asymptotically optimal rules if the distribution function of X is absolutely continuous. A detailed study is made of the pointwise, integral and uniform convergence of the Parzen-Rosenblatt and Loftsgaarden-Quesenberry density estimates. In addition, methods of estimating the conditional probability of error with a particular data set are given. For linear discrimination rules, local rules and two-step rules, estimates are found whose performance is bounded independently of the distribution of (X theta). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1976
- Accession Number
- ADA032738
Entities
People
- Luc P. J. A. Devroye
Organizations
- University of Texas at Austin