On asymptotic properties of bootstrap for AR(1) processes |
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| Institution: | 1. Department of Surgery, Duke University Medical Center, Durham, NC, 27710, USA;2. Department of Biostatistics and Bioinformatics, Duke University Medical Center, Durham, NC, 27710, USA;3. Department of Surgery, Division of Urology, Duke University Medical Center, Durham, NC, 27710, USA;4. Department of Surgery, Division of Pediatric Surgery, Duke University Medical Center, Durham, NC, 27710, USA;1. The Pennsylvania State University, United States;2. European Commission, Joint Research Centre, Italy |
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| Abstract: | We consider a first-order autoregressive process when the autoregressive parameter β may vary over the entire real line. The standard bootstrap approximation to the sampling distribution of the least squares estimator of β is shown to converge weakly to a random (i.e., nondegenerate) limit for the usual choice of the bootstrap sample size when β equals 1 or −1. The bootstrap approximation, however, is asymptotically valid in probability, or even almost surely, for suitably selected resample sizes, whatever β may be. |
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