Adaptive subsample estimation for multivariate normal distributions

Abstract

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.

Keywords:

• Kolmogorov-Smirnov statistic
• Minimum covariance determinant
• Minimum distance estimation
• Robust estimation
• Subsample selection

Additional information

Funding

The authors are grateful to the referee for the very detailed and thoughtful suggestions. This work is supported by National Natural Science Foundation of China (Grant No. 12171462, 11871033, 11871294).