Outlier Detection via a Block Diagonal Product Estimator

Outlier detection is a fundamental topic in robust statistics. Traditional outlier detection methods try to find a clean subset of given size, which is used to estimate the location vector and scatter matrix, and the outliers can be flagged by the Mahalanobis distance. However, methods such as the minimum covariance determinant approach cannot be applied directly to high-dimensional data, especially when the dimension of the sample is greater than the sample size. A novel fast detection procedure based on a block diagonal partition is proposed, and the asymptotic distribution of the modified Mahalanobis distance is obtained. The authors verify the specificity and sensitivity of this procedure by simulation and real data analysis in high-dimensional settings.