Search

The minimum covariance determinant (MCD) estimate is an important subsample method in robust statistics. It is commonly used to estimate parameters of multivariate normal distributions when outliers exist because of its good robustness properties. However, MCD has some disadvantages including low efficiency when there is no outliers and poor performance when there are clustered outliers. This paper first introduces an adaptive subsample method, and shows that the adaptive MCD estimator can possess both full asymptotic efficiency and maximum breakdown value. We then propose a minimum distance subsample estimate to handle the situations where there are clustered outliers. Simulation results indicate that the adaptive version of the minimum distance subsample estimate has satisfactory performance for various types of outliers. [ABSTRACT FROM AUTHOR]

Several methods have been proposed to solve the one-class classification problem for vectors. Three methods are mainly used: density estimation, boundary methods, and reconstruction methods. The focus here is on boundary methods. These methods include the k-center method, the nearest neighbor method, one-class support vector machine (OCSVM), and the support vector data description (SVDD). In industrial applications, like statistical process control (SPC), practitioners successfully used SVDD to detect anomalies or outliers in the process. However, when a multivariate process shifts, it occurs in either location or scale. This far, most of the research effort, like the OCSVM or SVDD, has focused on location (vectors or mean vectors). Several methods have been proposed recently to monitor the scale, i.e., the covariance matrix. Most of these methods deal with a full rank covariance matrix, i.e., a situation where the number of rational subgroups is larger than the number of variables. When the number of variables is nearly as large as, or larger than, the number of observations, most Shewhart-type charts are unable to solve this problem as the estimated covariance matrix is not full rank. This work will extend the one-class classification method using kernels to detect changes in the covariance matrix when the number of observations available is less than the number of variables. [ABSTRACT FROM AUTHOR]

Asymmetric models have been extensively studied in recent years, in situations where the normality assumption is not satisfied due to lack of symmetry of the data. Techniques for assessing the quality of fit and diagnostic analysis are important for model validation. This paper presents a study of the mean-shift method for detecting outliers in asymmetric normal regression models. Analytical solutions for the estimators of the parameters are obtained using the algorithm. Simulation studies and application to real data are presented, showing the efficiency of the method in detecting outliers. [ABSTRACT FROM AUTHOR]