Maximum trimmed likelihood estimator for multivariate mixed continuous and categorical data

In this article, we apply the maximum trimmed likelihood (MTL) approach [Hadi, A.S., Luceño, A., 1997. Maximum trimmed likelihood estimators: a unified approach, examples, and algorithms. Comput. Statist. Data Anal. 25, 251–272] to obtain the robust estimators of multivariate location and shape, especially for data mixed with continuous and categorical variables. The forward search algorithm [Atkinson, A.C., 1994. Fast very robust methods for the detection of multiple outliers. J. Amer. Statist. Assoc. 89, 1329–1339] is adapted to compute the proposed MTL estimates. A simulation study shows that the proposed estimator outperforms the classical maximum likelihood estimator when outliers exist in data. Real data sets are also used to illustrate the method and results of the detection of the outliers.