Non-Euclidean Conditional Expectation and Filtering

Cody Blaine Hyndman, Anastasis Kratsios

Publication date: 16 October 2017

Abstract: A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the non-convex optimization problem as transformations of Euclidean conditional expectation. This gives computationally tractable filtering equations for the dynamics of the intrinsic conditional expectation of a manifold-valued signal and is used to obtain accurate numerical forecasts of efficient portfolios by incorporating their geometric structure into the estimates.

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Numerical methods (including Monte Carlo methods) (91G60) Geometric probability and stochastic geometry (60D05) Filtering in stochastic control theory (93E11) Signal detection and filtering (aspects of stochastic processes) (60G35) Portfolio theory (91G10)

This page was built for publication: Non-Euclidean Conditional Expectation and Filtering

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6292628)