High-breakdown estimation of multivariate mean and covariance with missing observations

Area of Science:

• Multivariate Statistics
• Robust Statistics
• Data Analysis

Background:

• Estimating mean and covariance in incomplete multivariate data is essential for applications like factor analysis.
• The ER algorithm combines EM algorithm for missing data with M-estimators for robustness.
• The original ER algorithm can lack robustness, particularly in high-dimensional datasets with outliers.

Purpose of the Study:

• To propose robust alternatives to the ER algorithm for handling outliers in incomplete multivariate data.
• To enhance the robustness of mean and covariance estimation in high-dimensional settings.

Main Methods:

• Two novel approaches are presented: modifying the ER algorithm with a high-breakdown estimator as a starting point, and basing the ER algorithm's estimation step on a high-breakdown estimator.
• The Minimum Covariance Determinant (MCD) estimator and the t-biweight S-estimator are investigated as high-breakdown estimators.
• Simulated and real-world datasets are utilized for comparative analysis and illustration.

Main Results:

• The proposed modifications enhance the robustness of the ER algorithm in the presence of outliers, especially in high dimensions.
• High-breakdown estimators like MCD and t-biweight S-estimator effectively maintain robustness properties.
• Empirical evaluations demonstrate the improved performance of the suggested procedures compared to the original ER algorithm.

Conclusions:

• The developed robust estimation strategies provide effective solutions for outlier detection and handling in incomplete multivariate data.
• These methods are particularly valuable for improving the reliability of mean and covariance estimation in complex, high-dimensional datasets.
• The study highlights the importance of incorporating high-breakdown estimators for robust statistical inference.