Robust Estimation and Outlier Detection

  • Myung Geun Kim (Department of Applied Statistics, Seowon University, 231 Mochung-Dong, Chongju, Chung-Buk, 360-742, KOREA)
  • Published : 1994.12.01

Abstract

The conditional expectation of a random variable in a multivariate normal random vector is a multiple linear regression on its predecessors. Using this fact, the least median of squares estimation method developed in a multiple linear regression is adapted to a multivariate data to identify influential observations. The resulting method clearly detect outliers and it avoids the masking effect.

Keywords

References

  1. Appl. Statist. v.36 A New Graphical Method for Detecting Single and Multiple Outliers in Multivariate Data Bacon-Shone, J.;Fung, W. K.
  2. Outliers in Statistical Data(2nd ed.) Barnett, W.;Lewis, T.
  3. Appl. Statist. v.29 Robust Procedures in Multivariate Analysis Ⅰ: Robust Covariance Estimation Campbell, N. A.
  4. Appl. Statist. v.41 Sequential Application of Wilks's Multivariate Outlier Test Caroni, A.;Prescott, P.
  5. Technometrics v.26 Location of Several Outliers in Multiple-Regression Data Using Elemental Sets Hawkins, D. M.;Bradu, D.;Kass, G. V.
  6. Technometrics v.24 The Cholesky Factorization of the Inverse Correlation of Covariance Matrix in Multiple Regression Hawkins, D. M.;Eplett, W. J. R.
  7. Applied Multivariate Statistical Analysis Johnson, A. J.;Wichern, D. W.
  8. J. Amer. Statist. Ass. v.79 Least Median of Squares Regression Rousseeuw, P. J.
  9. Robust Regression and Outlier Detection Rousseeuw, P. J.;Leroy, A. M.
  10. J. Amer. Statist. Ass. v.85 Unmasking Multivariate Outliers and Leverage Points Rousseeuw, P. J.;van Zomeren, B. C.
  11. Multivariate Observations Seber, G. A. F.
  12. S-Plus for Dos : User's Manual
  13. Sankhya v.25 Multivariate Statistical Outliers Wilks, S. S.