Block Bootstrap for Poisson‐Sampled Almost Periodic Processes

25 Pages Posted: 24 Apr 2015

See all articles by Dominique Dehay

Dominique Dehay

University of Rennes II

Anna E. Dudek

AGH University of Science and Technology

Date Written: May 2015

Abstract

Let be an almost periodically correlated process and {N(t),t≥0} be a homogeneous Poisson process and {T,k≥1} be its jump moments. We assume that and {N(t),t≥0} are independent. Moreover, the process is not observed continuously but only in the time moments {T,k≥1}; In this paper, we focus on the estimation of the cyclic means of . The asymptotic normality of the rescaled error of the estimator is shown. Additionally, the bootstrap method based on the circular block bootstrap is proposed. The consistency of the bootstrap technique is proved, and the bootstrap pointwise and simultaneous confidence intervals for the cyclic means are constructed. The results are illustrated by a simulated data example.

Keywords: APC process, bootstrap, Poisson random sampling scheme, cyclic means, confidence interval, consistency

Suggested Citation

Dehay, Dominique and Dudek, Anna E., Block Bootstrap for Poisson‐Sampled Almost Periodic Processes (May 2015). Recent developments in bootstrap methods for dependent data, Vol. 36, Issue 3, pp. 327-351, 2015, Available at SSRN: https://ssrn.com/abstract=2598335 or http://dx.doi.org/10.1111/jtsa.12115

Dominique Dehay (Contact Author)

University of Rennes II

3 Allee Bobiere
Rennes, 35000
France

Anna E. Dudek

AGH University of Science and Technology

No Address Available

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