A1021
Title: Regularized projection depth
Authors: Filip Bocinec - Charles University (Czech Republic) [presenting]
Stanislav Nagy - Charles University (Czech Republic)
Hyemin Yeon - Kent State University (United States)
Abstract: Data depth is a powerful non-parametric concept that provides a center-outward ordering of data points and plays a key role in robust multivariate analysis. Among the many depth notions developed over the years, projection depth stands out as one of the most fundamental due to its strong theoretical properties and intuitive geometric interpretation. While several extensions of data depth have been proposed for functional data, projection depth suffers from degeneracy in infinite-dimensional spaces, making it inapplicable in its original form. A novel regularized projection depth that overcomes this limitation by appropriately constraining the set of admissible projection directions is introduced. This regularization prevents degeneracy and allows the depth to remain well-defined in functional settings. The theoretical properties of the proposed depth function are investigated in both multivariate and functional data frameworks. The practical applicability of the method is illustrated through examples involving real-world data.
