Bootstrap Percentile Confidence Intervals for Actual Error Rate in Linear Discriminant Analysis

Year 2009, Volume: 38 Issue: 3, 357 - 372, 01.03.2009

Cemal Atakan

Keywords

-

References

• Anderson, T. W. An introduction to multivariate statistical analysis, Second edition (John Wiley& Sons. Inc., New York, 1984).
• Davison, A. C. and Hinkley, D. V. Bootstrap methods and their application (Cambridge University Press, Cambridge, 1997).
• DiCicio, T. J. and Romano, J. P. A Review of bootstrap confidence intervals (with discus- sion), J. R. Statist. Soc. B. 50, 338–370, 1988.
• Efron, B. Bootstrap methods: Another look at the Jackknife, Ann. Math. Statist. 7, 1–26, Efron, B. Nonparametric standard errors and confidence intervals (with discussion), Canad. J. Statist. 9, 139–172, 1981.
• Efron, B. The Jackknife, the Bootstrap and other resampling plans (J. W. Arrowsmith Ltd., Bristol, England, 1982).
• Efron, B. Bootstrap confidence intervals for a class of parametric problems, Biometrica 72, –58, 1985.
• Efron, B. Better Bootstrap confidence intervals (with discussion), J. Amer. Statist. Assoc. , 171–200, 1987.
• Efron, B. and Gong, G. A Leisurely look at the Bootstrap, the Jackknife and Cross Valida- tion, The American Statistician 37, 36–48, 1983.
• Efron, B. and Tibshirani, R. Bootstrap methods for standard errors, confidence intervals and other measures of statistical accuracy(with discussion), Statist. Science 1, 54–77, 1986.
• Fisher, R. A. The Use of the multiple measurements in taxonomic problems, Annals of Eugenics 7, 179–188, 1936.
• Hall, P. Theoretical comparison of Bootstrap confidence intervals (with discussion), Ann. Statist. 16, 927–985, 1988.
• Hand, D. Recent advances in error rate estimation, Pattern Recognition 10, 211–222, 1986.
• Hand, D. Construction and assessment of classification rules (John Wiley & Sons, 1997).
• Hills, M. Allocation rules and their error rates, Journal of the Royal Statistical Society, Ser. B. 28, 1–20, 1966.
• John, S. Errors in discrimination, Ann. Math. Statist. 32, 1125–1144, 1961.
• Krzanowski, W. J. Data-based interval estimation of classification error rates, Journal of Applied Statistics 28 (5), 585–595, 2001.
• Kiers, H. A. L. Bootstrap confidence intervals for three way methods, J. Chemometrics 18, –36, 2004.
• Lachenbruch, P. A. An Almost unbiased method of obtaining confidence intervals for the probability of misclassification in discriminant analysis, Biometrics 23, 639–645, 1967.
• Lachenbruch, P. A. Discriminant analysis (Hafner Press., New York, 1975).
• Lachenbruch, P. A. and Mickey, M. R. Estimation of error rates in discriminant analysis, Technometrics 10, 1–11, 1968.
• McLachlan, G. J. An Asimptotic unbiased technique for estimation the error rates in dis- criminant analysis, Biometrics 30, 239-249, 1974.
• McLachlan, G. J. Confidence intervals for the conditional probability of misallocation in discriminant analysis, Biometrics 32, 161–167, 1975.
• McLachlan, G. J. Discriminant analysis and statistical pattern recognition (John Wiley & Sonsc Inc., New York, 1992).
• Okamoto, M. An asymptotic expansion for the distribution of the linear discriminant func- tion, Annals of Math. Statistics 34, 1286–1301, 1963.
• Sayre, J. W. The Distribution of the actual error rates in discriminant analysis, J. Amer. Statist. Assoc. 75, 201–205, 1980.
• Sitgreaves, R. Some results on the distribution of the W-classification statistics in Studies in Item Analysis and Prediction, H. Solomon ed., Stanford, Calif. Stanford University Press., –251, 1961.
• Smith, C. A. B. Some examples of discrimination, Annals of Eugenics 18, 272–282, 1947.
• Snapinn, S. M. An Evaluation of smoothed error rate estimators in discriminant analysis (Institute of Statistics Mimeo Series No. 1438, Dept. of Biostatistics, Univ. of N.C. at Chapel Hill, 1983).
• Timmerman, M. E. and Ter Braak, C. J. F. Bootstrap confidence intervals for principal re- sponse curves, Comput. Statis. and Data Anal. 52 (4), 1837–1849, 2007.
• Toussaint, G. T. Bibliography on estimation of misclassification, IEEE Trans. Inform. The- ory IT-20, 472–479, 1974.
• Wald, A. On Statistical problems arising in the classification of an individual into one of two groups, Ann. Math. Statist. 15, 145–162, 1944.
• Welch, B. L. Note on the discriminant functions, Biometrika 31, 218–220, 1939.
• Wasserman, L. All of nonparametric statistics (Springer, New York, USA, 2006).