Effects of different parameter estimators to error rate in discriminant analysis

Discriminant analysis is defined as a statistical technique that classifies a unit whose properties are measured, into one of the known finite numbers of populations. In this classifying process, an error occurs when the unit is classified to different population from its own population. This error is called the error rate or the probability of incorrect classification. It is desirable to minimize this error. This study focuses on determining the parameter estimation method that provides the minimum error rate, when the parameters of Weibull populations are not known. Maximum likelihood (ML), moments (MOM) and least squares (LS) methods are chosen from among parameter estimation methods. By a conducted simulation study, it is investigated that the error rate how is affected by the ML, LS and MOM estimates.

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P. A. Lachenburch, “Discriminant Analysis”, New York, Hafner, 1975.

G. A. F. Seber, “Multivariate Observations”, New York, John Wiley & Sons. Inc, 1984.

T. W. Anderson, “Introduction to Multivariate Statistical Analysis”, Wiley, New York, 1984.

B. L. Welch, “Note on Discriminant Functions”, Biometrika, 31, 218–220, 1939.

P. A. Lachenburch and R. Mickey, “Estimation of Error Rates in Discriminant Analysis”, Technometrics, 10, 1–11, 1968.

S. M. Snapin,” An Evaluation of Smooted Error Rate Estimators in Discriminant Analysis”, Institute of Statistics Miemeo Series, Chapel Hill, 1983.

M. Hills, “Allocation Rules and Their Error Rates”, J. Roy. Stat. Soc. B, 28, 1-31, 1966.

H. D. Biçer, “Discriminant analiysis in censored data: Weibull distribution case”, Doctoral dissertation, University of Ankara, 2011.

H. D. Biçer, C. Atakan and C. Biçer, “İki parametreli weibull dağılımına sahip kitlelerde diskriminant analizi”, NWSA Physical sciences, 6(4), 124-133, 2011.

C. A. B. Smith, “Some Examples of Discrimination”, Annals of Eugenics, 18, 272-282, 1978.

N. L. Johnson, S. Kotz and N. Balakrishnan, “Continuous univariate distributions”, New York, Wiley, 1995.

M. Tiryakioğlu and D. Hudak, “Unbiased estimates of the Weibull parameters by the linear regression method”, Journal of Materials Science, 43, 1914-1919, 2008.