Multivariate least-trimmed squares regression estimator

We propose a robust estimator in multivariate regression model based on the least-trimmed squares (LTS) estimator in univariate regression. We call this estimator the least-trimmed Mahalanobis squares distance (LTMS) estimator. The LTMS 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 LTMS estimator is a half-sample estimate and it has high breakdown point as does the LTS estimator in univariate case. We develop an algorithm for the LTMS estimator. Simulations are performed to compare the efficiencies of the LTMS estimate with other estimates and a numerical example is given to illustrate the effectiveness of the LTMS estimate in multivariate regressions.