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Article Dans Une Revue Electronic Journal of Statistics Année : 2017

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

Résumé

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.
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Dates et versions

hal-01343304 , version 1 (08-07-2016)
hal-01343304 , version 2 (04-01-2017)

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Citer

Dominique Dehay, Anna Dudek. Bootstrap for the second-order analysis of Poisson-sampled almost periodic processes. Electronic Journal of Statistics , 2017, 11 (1), pp.99-147. ⟨10.1214/17-EJS1225⟩. ⟨hal-01343304v2⟩
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