Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 6, November 2015, Pages: 602-609
Received: Oct. 12, 2015; Accepted: Oct. 26, 2015; Published: Dec. 10, 2015
Views 2975      Downloads 59
Author
I. Egbo, Department of Mathematics, Alvan Ikoku University of Education, Owerri, Nigeria
Article Tools
Follow on us
Abstract
The performance of four discriminant analysis procedures for the classification of observations from unknown populations was examined by Monte Carlo methods. The procedures examined were the Fisher Linear discriminant function, the quadratic discriminant function, a polynomial discriminant function and A-B linear procedure designed for use in situations where covariance matrices are equal. Each procedure was observed under conditions of equal sample sizes, equal covariance matrices, and in conditions where the sample was drawn from populations that have a multivariate normal distribution. When the population covariance matrices were equal, or not greatly different, the quadratic discriminant function performed similarly or marginally the same like Linear procedures. In all cases the polynomial discriminate function demonstrated the poorest, linear discriminant function performed much better than the other procedures. All of the procedures were greatly affected by non-normality and tended to make many more errors in the classification of one group than the other, suggesting that data be standardized when non-normality is suspected.
Keywords
Apparent Error Rates, Fisher’s Linear Discriminant, Quadratic Discriminant Function, A-B Discriminant Function, Polynomial Discriminant Function
To cite this article
I. Egbo, Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 6, 2015, pp. 602-609. doi: 10.11648/j.ajtas.20150406.32
Copyright
Copyright © 2015 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
Anderson, T.W. and Bahadur, R.R. (1962).Classification into two multivariate normal distributions with different covariance matrices. Annals of Mathematics Statistics, 33.420-431.
[2]
Barnard, M.M. (1935). The Secular variations of skull characteristics in four series of Egyptian skulls. Annals Eugenics, v. 6, 352-371.
[3]
Benerjee, K.S. & Marcus, L.F. (1965).In a Minimax Classification Procedure. Biometrics, 52, 654-654
[4]
Gilbert, S.E. (1968). “On Discrimination using Qualitative Variables” Journal of the American Statistical Association 1399-1418.
[5]
Gold Stein M. &Wolf (1977). On the problem of Bias multinomial classification. Biometrics 33, 325-331.
[6]
Hills, M. (1967). “Discriminantion and allocation with discrete data”, Applied Statistics. 16 237-250.
[7]
Lachenbruch, P.A. (1975) Discriminant Analysis. Hafner Press New York:
[8]
Marks, S. & Dunn, O.J. (1974). Discriminant functions when Covariance matrices are unequal. Journal of the American Statistical Association, 69, 555-559.
[9]
Martins, D.C., & Bradley, R.R. (1972). Probability Models, Estimation and Classification for Multivariate Dichotomous Populations, Biometrics,23, 203-221
[10]
Onyeagu S.I. (2003). Derivation of an optimal classification rule for discrete variables Journal of Nigerian Statistical Association, 73, 724-745.
[11]
Oluadare. S. (2011). Rubust Linear classifier for equal Cost Ratios of misclassification. CBN Journal of Applied Statistics.(2) (1)
[12]
Rao, C.R. (1965).Linear Statistical Inference and Its Applications: John Willey New York
[13]
Richard A.J. & Dean W.W. (1988).Applied Multivariate Statistical Analysis.4th edition Prentice Hall. Inc. New Jessey.
[14]
Smith, H.F. (1936). A discriminant function for plant selection. Ann. Eugn. 7, 240 – 250.
[15]
Tou, J.T. & Gonzalez, R. C. (1974).Pattern Recognition Principles. Reading, Mass.; Addison –Wesley.
[16]
Slah, B.Y. & Abdelwaheb Rebai (2007). Comparison between Statistical Approaches and linear programming for resolving classification problem. International Mathematics Forum, 2,(63), 3125-3141.
[17]
Egbo, I., Onyeagu, S.I. & Ekezie, D.D. (2014). A comparison of multinomial classification rules for binary variables. International Journal of Mathematical Science and Engineering Applications (IJMSEA),8, 141-157.
[18]
Ekezie, D.D. (2012). Comparison of seven Asymptotic Error Rate Expansion for the sample linear Discriminant function. Unpublished Ph.D thesis submitted to Department of Statistics, Imo State University, Owerri, Nigeria.
[19]
Egbo, I., Onyeagu, S.I. & Ekezie, D.D. (2014).A Comparison of Multivariate Discrimination of Binary Data. International Journal of Mathematics and Statistics Studies, 2(4), 40-61.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186