[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5351/CKSS.2005.12.1.039

A Robust Estimator in Multivariate Regression Using Least Quartile Difference

Jung Kang-Mo (Department of Informatics & Statistics, Kunsan National University)

Publication Information

Communications for Statistical Applications and Methods / v.12, no.1, 2005 , pp. 39-46 More about this Journal

Abstract

We propose an equivariant and robust estimator in multivariate regression model based on the least quartile difference (LQD) estimator in univariate regression. We call this estimator as the multivariate least quartile difference (MLQD) estimator. The MLQD estimator considers correlations among response variables and it can be shown that the proposed estimator has the appropriate equivariance properties defined in multivariate regressions. The MLQD estimator has high breakdown point as does the univariate LQD estimator. We develop an algorithm for MLQD estimate. Simulations are performed to compare the efficiencies of MLQD estimate with coordinatewise LQD estimate and the multivariate least trimmed squares estimate.

Keywords

Breakdown point; Equivariance; Least quartile difference estimator; Multivariate regression; Outliers;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	Ollila, E., Oja, H. and Hettmansperger, T. P. (2002). Estimates of regression coefficients based on the sign covariance matrix, Journal of the Royal Statistical Society Series B, 64, 447-466 DOI ScienceOn
2	Bickel, P. J. (1964). On some alternative estimates for shift in the p-variate one sample problem, Annals of Mathematical Statistics, 35, 1079-1090 DOI ScienceOn
3	Chakraborty, B. (1999). On multivariate median regression, Bernoulli, 5, 683-703 DOI ScienceOn
4	Croux, C., Rousseeuw, P. J. and Hossler; O. (1994). Generalized S-estimators, Journal of the American Statistical Association, 89, 1271-1281 DOI ScienceOn
5	Donoho, D. L. and Huber, P. J. (1983). The notion of breakdown point, In A Festschrift for Erich Lehmann, Edited by P. Bickel, K. Doksum and J. L. Hodges, 157-184, Wadsworth, Belmont, CA
6	Jung, K.-M. (2003). An equivariant and robust estimator in multivariate regression based on least trimmed squares, The Korean Communications in Statistics, 10, 1037-1046 DOI ScienceOn
7	Rao, C. R. (1988). Methodology based on the $L_1-norm$ in statistical inference, Sankhya, 50, 289-313
8	Rousseeuw, P. J. and Leroy, A. M. (1987). Robust Regression and Outlier Detection, John Wiley, New York