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Is the Brownian bridge a good noise model on the boundary of a circle?

Author

Listed:
  • Giacomo Aletti

    (Università degli Studi di Milano)

  • Matteo Ruffini

    (C/Diputacin, 303, Ático)

Abstract

In this paper, we study periodical stochastic processes, and we define the conditions that are needed by a model to be a good noise model on the circumference. The classes of processes that fit the required conditions are studied together with their expansion in random Fourier series to provide results about their path regularity. Finally, we discuss a simple and flexible parametric model with prescribed regularity that is used in applications, and we prove the asymptotic properties of the maximum likelihood estimates of model parameters.

Suggested Citation

  • Giacomo Aletti & Matteo Ruffini, 2017. "Is the Brownian bridge a good noise model on the boundary of a circle?," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 389-416, April.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:2:d:10.1007_s10463-015-0546-5
    DOI: 10.1007/s10463-015-0546-5
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    References listed on IDEAS

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    1. Asger Hobolth & Jan Pedersen & Eva Jensen, 2003. "A continuous parametric shape model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 227-242, June.
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    Cited by:

    1. Huang, Chunfeng & Li, Ao, 2021. "On Lévy’s Brownian motion and white noise space on the circle," Statistics & Probability Letters, Elsevier, vol. 171(C).

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