论文信息 - Multiple group linear discriminant analysis: robustness and error rate

Multiple group linear discriminant analysis: robustness and error rate

Discriminant analysis for multiple groups is often done using Fisher’s rule, and can be used to classify observations into different populations. In this paper, we measure the performance of classical and robust Fisher discriminant analysis using the Error Rate as a performance criterion.We were able to derive an expression for the optimal error rate in the situation of three groups. This optimal error rate serves then as a benchmark in the simulation experiments.

[1] B. Efron. Estimating the Error Rate of a Prediction Rule: Improvement on Cross-Validation , 1983 .

[2] J RousseeuwPeter,et al. A fast algorithm for the minimum covariance determinant estimator , 1999 .

[3] Katrien van Driessen,et al. A Fast Algorithm for the Minimum Covariance Determinant Estimator , 1999, Technometrics.

[4] C. R. Rao,et al. The Utilization of Multiple Measurements in Problems of Biological Classification , 1948 .

[5] B. Efron. How Biased is the Apparent Error Rate of a Prediction Rule , 1986 .

[6] David J. Hand,et al. A Handbook of Small Data Sets , 1993 .

[7] R. Fisher. THE STATISTICAL UTILIZATION OF MULTIPLE MEASUREMENTS , 1938 .

[8] Mia Hubert,et al. Fast and robust discriminant analysis , 2004, Comput. Stat. Data Anal..

[9] Douglas M. Hawkins,et al. High-Breakdown Linear Discriminant Analysis , 1997 .

[10] W. Fung,et al. High Breakdown Estimation for Multiple Populations with Applications to Discriminant Analysis , 2000 .

[11] C. Croux,et al. Robust linear discriminant analysis using S‐estimators , 2001 .

[12] Charles E. Heckler,et al. Applied Multivariate Statistical Analysis , 2005, Technometrics.

[13] R. Randles,et al. Generalized Linear and Quadratic Discriminant Functions Using Robust Estimates , 1978 .

[14] P. J. Rousseeuw,et al. Integrating a high-breakdown option into discriminant analysis in exploration geochemistry , 1992 .