A multivariate approach to dimension estimation on manifolds with triangle area U-statistics

For data on a manifold M ⊆ ℝᵐ and a point p ∈ M, this thesis introduces a multivariate estimator that leverages angle- and triangle area-based U-statistics (U₁, V₁, V₂) to assess the intrinsic dimension of M at p. By considering the variance of angles formed by pairs of nearby data points, and the m...