Asymptotic Evaluation of the Probabilities of Misclassification by Linear Discriminant Functions

Abstract

Linear discriminant functions are used to classify an observation as coming from one of two normal populations with common covariance matrices and different means when samples are used to estimate the parameters of the distributions. Okamoto's asymptotic expansion of the distribution of the classification statistic W is compared with Anderson's expansion for the Studentized W (that is, W standardized by estimates of its mean and standard deviation). Some numerical evaluations of the term of order of the reciprocal of the sample sizes is given. The uses of the two approximate distributions are discussed.

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Document Details

Document Type
Technical Report
Publication Date
Sep 28, 1972
Accession Number
AD0749972

Entities

People

  • Theodore W. Anderson

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Asymptotic Series
  • Confidence Limits
  • Contracts
  • Covariance
  • Data Science
  • Discriminant Analysis
  • Distribution Functions
  • Information Science
  • Military Research
  • Normal Distribution
  • Observation
  • Probability
  • Probability Distributions
  • Security
  • Standards
  • Statistics
  • Test And Evaluation

Fields of Study

  • Mathematics

Readers

  • Regression Analysis.
  • Statistical inference.