Introduces Riemannian AR(1) model on manifolds and proves SLLN for Fréchet means of dependent data to enable parameter estimation.
On the Kolmogorov-Feller weak law of large numbers for the Fr\'echet mean on non-compact symmetric spaces
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abstract
We prove the Kolmogorov-Feller weak law of large numbers for sample Fr\'echet means on non-compact symmetric spaces. The result covers independent, non-identically distributed data, extending beyond the i.i.d. setting. Examples of symmetric positive-definite matrices and product symmetric spaces are provided.
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2026 1verdicts
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Autoregressive Processes on Riemannian Manifolds
Introduces Riemannian AR(1) model on manifolds and proves SLLN for Fréchet means of dependent data to enable parameter estimation.