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Bootstrap methods for dependent data: A review
Jens-Peter Kreiss,Efstathios Paparoditis 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.4
This paper gives a review on a variety of bootstrap methods for dependent data. The main focus is not on an exhaustive listing and description of bootstrap procedures but on general principles which should be taken into account when selecting a particular bootstrap procedure in order to approximate the (properly standardized) distribution of a statistic of interest. Questions are considered related to which dependence properties of the underlying data generating process asymptotically influence the distribution of the statistic of interest and which dependence properties (or even which process) a particular bootstrap method really mimics. For answering these questions we introduce the concept of a companion stochastic process. As statistics we consider generalized means, and integrated periodogram statistics (including ratio statistics) as well as nonparametric estimators.
Simultaneous bootstrap for all three parameters in random coefficient autoregressive models
Thorsten Fink,Jens-Peter Kreiss 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.3
In this paper we consider autoregressive processes with random coefficients and developbootstrap approaches that asymptotically work for the distribution of estimated autoregressiveparameter as well as for the distribution of estimated variances of the innovationnoise and the disturbance noise. We discuss how to obtain approximative residuals of theprocess and how to separate between the innovation and the disturbance noise in orderto be able to extend the classical residual bootstrap for autoregressive processes to the situationconsidered in this paper. Thereafter, we propose a wild bootstrap procedure as avariation of the residual bootstrap that uses estimated densities of the innovation and thedisturbance noise to generate bootstrap replicates of the data generating process. The consistencyof the bootstrap approaches is established and their performance is illustrated bya simulation study.