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Non-Euclidean Conditional Expectation and Filtering

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  • Anastasis Kratsios
  • Cody B. Hyndman

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.

Suggested Citation

  • Anastasis Kratsios & Cody B. Hyndman, 2017. "Non-Euclidean Conditional Expectation and Filtering," Papers 1710.05829, arXiv.org, revised Sep 2018.
  • Handle: RePEc:arx:papers:1710.05829
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    File URL: http://arxiv.org/pdf/1710.05829
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    References listed on IDEAS

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