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Nonparametric estimation for stationary and strongly mixing processes on Riemannian manifolds

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Abstract

In this paper, nonparametric estimation for a stationary strongly mixing and manifold-valued process \((X_j)\) is considered. In this non-Euclidean and not necessarily i.i.d setting, we propose kernel density estimators of the joint probability density function, of the conditional probability density functions and of the conditional expectations of functionals of \(X_j\) given the past behavior of the process. We prove the strong consistency of these estimators under sufficient conditions, and we illustrate their performance through simulation studies and real data analysis.

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Acknowledgements

The authors thank the reviewers for a most careful reading of the manuscript and constructive comments and remarks.

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Authors and Affiliations

  1. IMSP, Université d’Abomey-Calavi (UAC), Dangbo, Benin

    Amour T. Gbaguidi Amoussou & Carlos Ogouyandjou

  2. FAST, Université d’Abomey-Calavi, Abomey-Calavi, Benin

    Freedath Djibril Moussa

  3. Université Gaston Berger, Dakar, Senegal

    Mamadou Abdoul Diop

Authors
  1. Amour T. Gbaguidi Amoussou
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  2. Freedath Djibril Moussa
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  3. Carlos Ogouyandjou
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  4. Mamadou Abdoul Diop
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Corresponding author

Correspondence to Freedath Djibril Moussa.

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Gbaguidi Amoussou, A.T., Djibril Moussa, F., Ogouyandjou, C. et al. Nonparametric estimation for stationary and strongly mixing processes on Riemannian manifolds. Commun. Math. Stat. 10, 599–621 (2022). https://doi.org/10.1007/s40304-020-00237-0

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  • DOI: https://doi.org/10.1007/s40304-020-00237-0

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