Block Bootstrap for Poisson‐Sampled Almost Periodic Processes

Let {X(t),t∈R} be an almost periodically correlated process and {N(t),t≥0} be a homogeneous Poisson process and {Tk,k≥1} be its jump moments. We assume that {X(t),t∈R} and {N(t),t≥0} are independent. Moreover, the process {X(t),t∈R} is not observed continuously but only in the time moments {Tk,k≥1};...

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Veröffentlicht in:	Journal of time series analysis 2015-05, Vol.36 (3), p.327-351
Hauptverfasser:	Dehay, Dominique, Dudek, Anna E.
Format:	Artikel
Sprache:	eng
Schlagworte:	APC process bootstrap Bootstrap mechanism Bootstrap method confidence interval consistency Correlation cyclic means Error Estimation Mathematical analysis Mathematics Poisson random sampling scheme Sampling Statistics Studies Time series
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container_title	Journal of time series analysis
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creator	Dehay, Dominique Dudek, Anna E.
description	Let {X(t),t∈R} be an almost periodically correlated process and {N(t),t≥0} be a homogeneous Poisson process and {Tk,k≥1} be its jump moments. We assume that {X(t),t∈R} and {N(t),t≥0} are independent. Moreover, the process {X(t),t∈R} is not observed continuously but only in the time moments {Tk,k≥1}; In this paper, we focus on the estimation of the cyclic means of {X(t),t∈R}. 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.
doi_str_mv	10.1111/jtsa.12115
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We assume that {X(t),t∈R} and {N(t),t≥0} are independent. Moreover, the process {X(t),t∈R} is not observed continuously but only in the time moments {Tk,k≥1}; In this paper, we focus on the estimation of the cyclic means of {X(t),t∈R}. 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. 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subjects	APC process bootstrap Bootstrap mechanism Bootstrap method confidence interval consistency Correlation cyclic means Error Estimation Mathematical analysis Mathematics Poisson random sampling scheme Sampling Statistics Studies Time series
title	Block Bootstrap for Poisson‐Sampled Almost Periodic Processes
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