Bootstrap for the second-order analysis of Poisson-sampled almost periodic processes

نویسندگان

  • Dominique Dehay
  • Anna Dudek
  • Anna E. Dudek
چکیده

In this paper we consider a continuous almost periodically correlated process {X(t), t ∈ R} that is observed at the jump moments of a stationary Poisson point process {N(t), t ≥ 0}. The processes {X(t), t ∈ R} and {N(t), t ≥ 0} are assumed to be independent. We define the kernel estimators of the Fourier coefficients of the autocovariance function of X(t) and investigate their asymptotic properties. Moreover, we propose a bootstrap method that provides consistent pointwise and simultaneous confidence intervals for the considered coefficients. Finally, to illustrate our results we provide a simulated data example. AMS 2000 subject classifications: Primary : 62M15. Secondary : 62G09, 62G05, 62G20.

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تاریخ انتشار 2017