Testing the Optimality of Two Different Non-Parametric Discriminant Methods

  • Evelyn N. Okeke Depatment of Mathematics & Statistics, Federal University, Wukari, Taraba State, Nigeria
  • Uchenna J. Okeke Depatment of Mathematics & Statistics, Federal University, Wukari, Taraba State, Nigeria
Keywords: Variance-covariance matrix, Data depth, Spatial or L1 depth, Linear Discriminant analysis, Probability of Misclassification(PMC).


This paper aims at comparing the concept of data depth to classification and classification by projection pursuit using method of linear discriminant function. These two methods allow the extension of univariate concepts to the field of multivariate analysis. In particular they open the possibility of non-parametric methods to be used in multivariate data analysis. In this study, six simulated and one real life data sets were studied and, we observed that projection pursuit method is more optimal in classifying objects into their original groups.


[1] J. Tukey. (1975) Mathematics and picturing data. In R. James, ed., Proceedings of the 1994 International congress of mathematicians. Vancouver vol 2, 523-531.
[2] D. L.Donoho and M. Gasko. (1992). “Breakdown properties of multivariate location estimates based on halfspace depth and projected outlyingness.” Annals of Statistics,20(4), pp. 1803-1827.
[3] P. Chaudhuri. (1996). “On a geometric notion of quantiles for multivariate data.” Journal of American Statistical Association 91, pp. 862-872.
[4] R. Y. Liu. (1992). Data depth and multivariate rank tests. In L1-statistical analysis and related methods (Neuch tel, 1992), pages 279-294. North-Holland, Amsterdam.
[5] Y. Zuo and R. Serfling. (2000). “General notions of statistical depth function.” Annals of Statistics 28, 461-482.
[6] P.J. Rousseew and M. Hubert. (1990). “Regression depth (with discussion).” Journal of the American Statistical Association. 94, pp. 388-433.
[7] H. Oja. (1983). “Discriptive statistics for multivariate distributions.” Statistics and Probability Letters. 1, pp. 327-332.
[8] R. Y. Liu. (1990). “On a notion of data depth based on random simplices.” Annals of Statistics. 18(1):405- 414. Analysis, 20:669-687.
[9] V. Barnet. (1976). “The ordering of multivariate data.” Journal of the Royal Statistical Society ser. A 139, pp. 318- 355
[10] Z. Y. Chen. “Robust linear discriminant procedures using projection pursuit methods.” PhD Dissertation, University of Michigan, USA, 1989.
[11] C. Posse. (1995). “Projection pursuit exploratory data analysis.”Computational Statistics and Data lib.dr.iastate.edu/cgi/viewcontent.cgi?article=2440&content=rtd
[12] P. J. Huber. (1985). “Projection pursuit.”.Annals of Statistics, 13920,pp. 435-525.With discussion. projecteuclid.org/Euclid.aos/1176349530
[13] M. Goldstein. (1987). [a review of multivariate analysis]. Comment. Statistical Science, 2(4):418-420.
[14] M. C. Jones. (1983). The projection pursuit algorithm for exploratory data Analysis, PhD Thesis, University of Bath.
[15] C. Gini. (1916). II concetto di transvariazione e le sue prime applicazioni. Giornale degli economisti Rivista di statistica.
[16] D.D. Ekezie. “A biometric study of oil palm (Elaeis guneensis Jacq) nursery characteristics and yield by the method of multivariate analysis.” Ph.D seminar paper, Nnamdi Azikiwe University Awka, Nigeria, Oct. 2010.