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Original Articles

The Relationship in Terms of Asymptotic Mean Square Error Between the Separate Problems of Estimating each of the Three Types of Error Rate of the Linear Discriminant Function

Pages 569-575 | Published online: 09 Apr 2012

References

  • Anderson , T. W. 1951 . Classification by multivariate analysis . Psychometrika , 16 : 31 – 50 .
  • Broffitt , James D. 1969 . Estimating the probability of misclassification based on discriminant function techniques , Ph.D. dissertation Fort Collins : Colorado State University. .
  • Hills , M. 1966 . Allocation rules and their error rates . J. Roy. Statist. Soc. Ser B , 28 : 1 – 32 .
  • Hoel , G. and Peterson , R. P. 1949 . A solution to the problem of optimum allocation . Ann. Math. Statist. , 20 : 433 – 438 .
  • Lachenbruch , P. A. 1965 . Estimation of error rates in discriminant analysis , Ph.D. dissertation Los Angeles : University of California. .
  • Lachenbruch , P. A. 1967 . An almost unbiased method of obtaining confidence intervals for the probability of misclassification in discriminant analysis . Biometrics , 23 : 639 – 645 .
  • Lachenbruch , P. A. 1968 . On expected probabilities of misclassification in discriminant analysis, necessary sample size, and a relation with the multiple correlation coefficient . Biometrics , 24 : 823 – 834 .
  • Lachenbruch , P. A. and Mickey , M. R. 1968 . Estimation of error rates in discriminant analysis . Technometrics , 10 : 1 – 11 .
  • McLachlan , G. J. 1973 . The errors of allocation and their estimators in the two-population discrimination problem , Ph.D. dissertation Australia : University of Queensland. .
  • McLachlan , G. J. 1974 . An asymptotic unbiased technique for estimating the error rates in discriminant analysis . Biometrics , 30 : 239 – 249 .
  • McLachlan , G. J. 1974 . Estimation of the errors of misclassification on the criterion of asymptotic mean square error . Technometrics , 16 : 255 – 260 .
  • McLachlan , G. J. 1974 . An asymptotic expansion of the expectation of the estimated error rate in discriminant analysis . Austral J. Statist. , 15 : 210 – 214 .
  • Okamoto , M. 1963 . An asymptotic expansion for the distribution of the linear discriminant function . Ann. Math. Statist. , 34 : 1286 – 1301 . Correction: (1968). Ann. Math. Statist., 39, 1358–1359
  • Pogue , Richard E. 1966 . Some investigations of multivariate discrimination procedures, with applications to diagnosis in clinical electrocardiography , Ph.D. dissertation Minneapolis : University of Minnesota. .
  • Sedransk , N. and Okamoto , M. 1971 . Estimation of the probabilities of misclassification for a linear discriminant function in the univariate normal case . Ann. Inst. Statist. Math. , 23 : 419 – 435 .
  • Sorum , M. 1971 . Estimating the conditional probability of misclassification . Technometrics , 13 : 333 – 343 .
  • Sorum , M. 1972 . Three probabilities of misclassification . Technometrics , 14 : 309 – 316 .
  • Sorum , M. 1972 . Estimating the expected and the optimal probabilities of misclassification . Technometrics , 14 : 935 – 943 .
  • Sorum , M. 1973 . Estimating the expected probability of misclassification for a rule based on the linear discriminant function: univariate normal case . Technometrics , 15 : 329 – 339 .
  • Welch , B. L. 1939 . Note on discriminant functions . Biometrika , 31 : 218 – 220 .

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