• DocumentCode
    930739
  • Title

    Risk estimation for nonparametric discrimination and estimation rules: A simulation study (Corresp.)

  • Author

    Penrod, C.S. ; Wagner, T.J.

  • Volume
    25
  • Issue
    6
  • fYear
    1979
  • fDate
    11/1/1979 12:00:00 AM
  • Firstpage
    753
  • Lastpage
    758
  • Abstract
    The designer of a nonparametric discrimination or estimation procedure is almost always interested in the conditional risk of his procedure, or nde, conditioned on the available data. Unfortunately, L_{n} , the risk conditioned on a data set containing n observations, cannot be computed without exact knowledge of the underlying probability distribution functions. Since such knowledge is unavailable, the designer must be content with estimates of L_{n} . Two such estimates are the deleted estimate, L_{n}^{D} , and the holdout estimate, L_{n}^{H} . This paper presents the results of an experimental study of these two estimates and compares these results with some recently obtained distribution.free theoretical results. Among other things, the experimental data indicates that for k -nearest neighbor rules in {\\bf R^{1}} with several examples of underlying distributions, P \\{ \\mid L_{n} - L^{D}_{n} \\mid \\geq \\epsilon \\} \\geq 2e^{-2 \\epsilon^{2}n} mbox{ P \\{ \\mid L_{n} - L^{H}_{n} \\mid \\geq \\epsilon \\} 2e^{-2 \\epsilon^{2} \\sqrt{n}} .}
  • Keywords
    Nonparametric detection; Nonparametric estimation; Pattern classification; Distributed computing; Error analysis; Error probability; Feature extraction; Nearest neighbor searches; Notice of Violation; Pattern recognition; Probability distribution; Upper bound;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.1979.1056101
  • Filename
    1056101