Robust Inference after Random Projections via Hellinger Distance for Location-Scale Family.

Area of Science:

• Data Science
• Statistics
• Machine Learning

Background:

• Contemporary business and industry extensively utilize big data and streaming data.
• Random projections are commonly employed for data dimension reduction, creating compressed data.
• Compressed data often contains anomalies (heterogeneity, outliers, round-off errors) difficult to detect due to volume and processing constraints.

Purpose of the Study:

• To present a novel, robust, and efficient methodology for analyzing compressed data.
• To address the challenges posed by anomalies in high-dimensional, compressed datasets.
• To demonstrate the feasibility and effectiveness of robust estimation procedures in this context.

Main Methods:

• Utilizing Hellinger distance as a core analytical tool.
• Employing large sample methods for theoretical validation.
• Conducting numerical experiments to assess performance and robustness.

Main Results:

• The proposed Hellinger distance-based methodology effectively analyzes compressed data.
• Robust estimation procedures are demonstrated to be feasible for routine use.
• The study elucidates the role of double limits in understanding the efficiency and robustness of the method.

Conclusions:

• A new robust and efficient method for analyzing compressed big data using Hellinger distance is established.
• The findings support the routine application of robust estimation in analyzing complex, high-volume datasets.
• The work contributes to understanding data analysis challenges and solutions in big data environments.