Electronic Journal of Statistics

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

Dominique Dehay and Anna E. Dudek

Full-text: Open access

Abstract

In this paper we consider a continuous almost periodically correlated process $\{X(t),t\in\mathbb{R}\}$ that is observed at the jump moments of a stationary Poisson point process $\{N(t),t\geq0\}$. The processes $\{X(t),t\in\mathbb{R}\}$ and $\{N(t),t\geq0\}$ 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.

Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 99-147.

Dates
Received: July 2016
First available in Project Euclid: 23 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1485162022

Digital Object Identifier
doi:10.1214/17-EJS1225

Mathematical Reviews number (MathSciNet)
MR3599801

Zentralblatt MATH identifier
06678126

Subjects
Primary: 62M15: Spectral analysis
Secondary: 62G09: Resampling methods 62G05: Estimation 62G20: Asymptotic properties

Keywords
Block bootstrap consistency Fourier coefficients of autocovariance function irregular sampling nonstationary process

Citation

Dehay, Dominique; Dudek, Anna E. Bootstrap for the second-order analysis of Poisson-sampled almost periodic processes. Electron. J. Statist. 11 (2017), no. 1, 99--147. doi:10.1214/17-EJS1225. https://projecteuclid.org/euclid.ejs/1485162022


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