Development of Two Methods for Estimating High-Dimensional Data in the Case of Multicollinearity and Outliers

Résumé

High-dimensional problems involve datasets or models characterized by a substantial number of variables or parameters prevalent across various domains such as statistics, machine learning, optimization, physics, and engineering. Challenges in these scenarios include computational complexity, data sparsity, over-fitting, and the curse of dimensionality. This study introduces two innovative techniques that combine the Random Forest machine learning approach with both the least absolute shrinkage and selection operator and the elastic net, which are statistical methodologies tailored to address high-dimensional challenges. We compared performance evaluations of these hybrid methods against traditional statistical approaches and standalone machine learning methods. The assessment is conducted using goodness-of-fit measures and involves both Monte Carlo simulation and a real-world application. The findings show that the strategies proposed in this study exhibit superior performance compared to conventional approaches when tackling high-dimensional challenges.

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