Diskriminant analizinde gerçek hata oranına ilişkin güven aralığı için bir simülasyon çalışması

Bu çalışmada, gerçek hata oranına ilişkin M tahmin edicisine dayalı mevcut olan analitik güven aralığı ifadelerinden elde edilen sonuçlar, bootstrap tekniği ile elde edilen sonuçlarla karşılaştırılmaktadır. Karşılaştırma sonucunda bootstrap tekniğinin daha dar aralıklar verdiği görülmektedir.

A simulation study for the confidence interval based on the actual error rate in discriminant analysis

In this study, the existing analitical confidence intervals based on the actual error rate estimator M compared with the bootstrap by simulation. It has been observed that bootstrap results give norrower intervals.

___

[1] Welch. B. L. Note on the Discriminant Functions. Biometrica, 31, 218-220, (1939).

[2] Anderson, T. W. An Introduction to Multivariate Satistical Analysis, Second edition, John Wiley& Sons. Inc., New York, (1984).

[3] Lachenbruch, P. A. Discriminant Analysis. Hafner Press., New York, (1975).

[4] Smith, C.A.B. Some Examples of Discrimination, Annals of Eegenics, 18, 272-282, (1947).

[5] Hills, M. Allocation Rules and their Error Rates”, Journal pf the Royal Statistical Society, Ser. B, 28, 1-20, (1966).

[6] Lachenbruch, P. A. & Mickey, M. R. Estimation of Error Rates in Discriminant Analysis. Technometrics, 10, 1-11, (1968).

[7] Seber, G. A. F. Multivariate Observations. John Wiley & Sons. Inc., (1984).

[8] Wald, A. On Statistical Problems Arising in the Clasification of an Individual into One of Two Groups, Annals of Mathematical Statistics, 15, 145-162, (1944).

[9] Snapinn, S. M. An Evaluation of Smoothed Error Rate Estimators in Discriminant Analysis, Institute of Statistics Mimeo Series No:1483, University North Carolina at Chapel Hill, (1983).

[10] Atakan, C. Ve Öztürk, F. Comparisons of Some Smoothed Error Rate Estimators in Discriminant Analysis, Hacettepe Bulletin of Natural Sciences and Engineering Series B, 27, 51-64, (1998a).

[11] Atakan, C., Öztürk, F. Diskriminant Analizinde Hata Oranı Tahmin Edicilerinin Yan ve Varyanslarının Jackknife ve Bootstrap Tahminleri, Celal Bayar Üniversitesi Fen-Edebiyat Fakültesi Dergisi, Fen Bilimleri Serisi(Matematik),4, 14-20, (1998b).

[12] Meaux, L. M., Young, D. M., Seaman, J. W. A Comparision of Parametric Conditional Error Rate Estimators for the Two-Group Linear Discriminant Function, J. Statist. Comput. Simul., Vol.69, 277-291, (2001).

[13] McLachlan, G. J. (1974). An Asimptotic Unbiased Technique for Estimation the Error Rates in Discriminant Analysis. Biometrics, 30, 239-249, (1974).

[14] McLachlan, G. J. Discriminant Analysis and Statistical Pattren Recognition, John Wiley & Sonsc Inc., New York, (1992).

[15] McLachlan, G. J. (1975). Confidence Intervals for the Conditional Probability of Misallocation in Discriminant Analysis, Biometrics, 32, 161-167, (1975).

[16] Efron, B. Bootstrap Methods: Another look at the Jackknife, Annals of Stat., 7, 1-26, (1979).

[17] Efron, B. The Jackknife, the Bootstrap and Other Resampling Plans. J. W. Arrowsmith ltd., Bristol, England, (1982).

[18] Efron, B. & Gong. A Leisurely Look at the Bootstrap, the Jackknife and Cross Validation. The American Statistician, 37, 36-48, (1983).