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Nonparametric estimation problem for a time-periodic signal in a periodic noise


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  • Dehay, D.
  • El Waled, K.
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    In this paper we construct a kernel estimator of a periodic signal when the observation follows the model dζt=f(t)dt+σ(t)dWt, where f,σ:R→R are continuous periodic and {Wt,t≥0} is a Brownian motion. We state its consistency as well as the asymptotic normality.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 2 ()
    Pages: 608-615

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:608-615

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    Keywords: Periodic signal; Kernel estimation; Continuous time; Periodic variance; Black–Scholes–Merton model;


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    1. Jankunas, Andrius & Khasminskii, Rafail Z., 1997. "Estimation of parameters of linear homogeneous stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 205-219, December.
    2. Reinhard Höpfner & Yury Kutoyants, 2010. "Estimating discontinuous periodic signals in a time inhomogeneous diffusion," Statistical Inference for Stochastic Processes, Springer, vol. 13(3), pages 193-230, October.
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