You are here

Performance of linear discriminant analysis using di erent robust methods

Journal Name:

Publication Year:

Abstract (2. Language): 
This study aims to combine the new deterministic minimum covariance determinant (DetMCD) algorithm with linear discriminant analysis (LDA) and compare it with the fast minimum covariance determinant (FastMCD), fast consistent high breakdown (FCH), and robust FCH (RFCH) algorithms. LDA classi es new observations into one of the unknown groups and it is widely used in multivariate statistical analysis. The LDA mean and covariance matrix parameters are highly in uenced by outliers. The DetMCD algorithm is highly robust and resistant to outliers and it is constructed to overcome the outlier problem. Moreover, the DetMCD algorithm is used to estimate location and scatter matrices. The DetMCD, FastMCD, FCH, and RFCH algorithms are applied to estimate misclassi cation probability using robust LDA. All the algorithms are expected to improve the LDA model for classi cation purposes in banks, such as bankruptcy and failures, and to distinguish between Islamic and conventional banks. The performances of the estimators are investigated through simulation and actual data..
284
298

REFERENCES

References: 

[1] Mufda Jameel Alrawashdeh, Shamsul Rijal Muhammad Sabri, and Mohd Tahir Ismail.
Robust linear discriminant analysis with nancial ratios in special interval.
Applied Mathematical Sciences, 6(121):6021{6034, 2012.
[2] Billor, Nedret, Ali S Hadi, and Paul F Velleman. Bacon: blocked adaptive computationally
ecient outlier nominators. Computational Statistics and Data Analysis,
34(3):279{298, 2000.
[3] Chork, CY, and Peter J Rousseeuw. Integrating a high-breakdown option into discriminant
analysis in exploration geochemistry. Journal of Geochemical Exploration,
43(3):191{203, 1992.
REFERENCES 297
[4] Croux, Christophe, and Catherine Dehon. Analyse canonique base sur des estimateurs
robustes de la matrice de covariance. Revue de statistique applique, 50(2):5{26, 2002.
[5] Croux, Christophe, Peter Filzmoser, and Kristel Joossens. Classication eciencies
for robust linear discriminant analysis. Statistica Sinica, 18(2):581{599, 2008.
[6] Croux, Christophe, Sarah Gelper, and Koen Mahieu. Robust exponential smoothing
of multivariate time series. Computational Statistics and Data Analysis, 54(12):2999{
3006, 2010.
[7] Croux, Christophe, and Gentiane Haesbroeck. Principal component analysis based
on robust estimators of the covariance or correlation matrix: in
uence functions and
eciencies. Biometrika, 87(3):603{618, 2000.
[8] Devlin, S. J., Gnanadesikan, R., Kettenring, and J. R. Robust estimation of dispersion
matrices and principal components. Journal of the American Statistical Association,
76(374):354{362, 1981.
[9] Fekri, M, and Anne Ruiz-Gazen. Robust weighted orthogonal regression in the errorsin-
variables model. Journal of the American Statistical Association, 88(1):89{108,
2004.
[10] Hawkins, D.M., Olive, and D.J. Improved feasible solution algorithms for high breakdown
estimation. Computational Statistics and Data Analysis, 30:1{11, 1999.
[11] Hawkins, Douglas M, and Georey J McLachlan. High-breakdown linear discriminant
analysis. Journal of the American statistical association, 92(437):136{143, 1997.
[12] He, Xuming, and Wing K Fung. High breakdown estimation for multiple populations
with applications to discriminant analysis. Journal of Multivariate Analysis,
72(2):151{162, 2000.
[13] Hubert, Mia, and K Vanden Branden. Robust methods for partial least squares
regression. Journal of Chemometrics, 17(10):537{549, 2003.
[14] Hubert, Mia, and Katrien Van Driessen. Fast and robust discriminant analysis. Com-
putational Statistics and Data Analysis, 45(2):301{320, 2004.
[15] Hubert, Mia, and Peter J Rousseeuw. Robust regression with both continuous and
binary regressors. Journal of Statistical Planning and Inference, 57(1):153{163, 1997.
[16] Hubert, Mia, Peter J Rousseeuw, and Stefan Van Aelst. High-breakdown robust
multivariate methods. Statistical Science, 23(1):92{119, 2008.
[17] Hubert, Mia, Peter J Rousseeuw, and Karlien Vanden Branden. Robpca: a new
approach to robust principal component analysis. Technometrics, 47(1):64{79, 2005.
REFERENCES 298
[18] Hubert, Mia, Peter J Rousseeuw, and Tim Verdonck. A deterministic algorithm
for robust location and scatter. Journal of Computational and Graphical Statistics,
21(3):618{637, 2012.
[19] Hubert, Mia, and Sabine Verboven. A robust pcr method for highdimensional regressors.
Journal of Chemometrics, 17(89):438{452, 2003.
[20] Maronna, Ricardo A, and Ruben H Zamar. Robust estimates of location and dispersion
for high-dimensional datasets. Technometrics, 44(4):307{317, 2002.
[21] David J. Olive and Douglas M. Hawkins. Robust multivariate location and dispersion.
Southern Illinois University and University of Minnesota, 2010.
[22] Pison, Greet, and et al. Robust factor analysis. Journal of Multivariate Analysis,
84(1):145{172, 2003.
[23] Rousseeuw and Peter J. Least median of squares regression. Journal of the American
statistical association, 79(388):871{880, 1984.
[24] Rousseeuw, Peter J, and Christophe Croux. Alternatives to the median absolute
deviation. Journal of the American Statistical Association, 88(424):1273{1283, 1993.
[25] Rousseeuw, Peter J, and Katrien Van Driessen. A fast algorithm for the minimum
covariance determinant estimator. Technometrics, 41(3):212{223, 1999.
[26] Rousseeuw, Peter J, and Bert C Van Zomeren. Unmasking multivariate outliers and
leverage points. Journal of the American Statistical Association, 85(411):633{639,
1990.
[27] Todorov and Valentin. Robust selection of variables in linear discriminant analysis.
Statistical Methods and Applications, 15(3):395{407, 2007.
[28] S. Visuri, H. Oja, and V. Koivunen. Sign and rank covariane matrices. J. Statist.
Plann. Inference, 91:557575, 2000.
[29] Wiegand, Patrick, Randy Pell, and Enric Comas. Simultaneous variable selection
and outlier detection using a robust genetic algorithm. Chemometrics and Intelligent
Laboratory Systems, 98(2):108{114, 2009.
[30] Jianfeng Zhang, David J. Olive, and Ping Ye. Robust covariance matrix estimation
with canonical correlation analysis. International Journal of Statistics and Probability,
1(2):119{136, 2012.

Thank you for copying data from http://www.arastirmax.com