Bootstrap methods for dependent data: A review

Kreiß, Jens-Peter; Paparoditis, Efstathios

doi:10.1016/j.jkss.2011.08.009

Cited by 95 publications

(53 citation statements)

References 87 publications

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“…In some recent surveys, Bühlmann (2002), Politis (2003) and Kreiss and Paparoditis (2011) revisited some bootstrap methods, such as moving block bootstrap and sieve bootstrap, which are mainly applied to univariate or multivariate dependent data. In the future research, we intend to extend bootstrap methods for functional time series.…”

Section: Resultsmentioning

confidence: 99%

Resampling Techniques for Estimating the Distribution of Descriptive Statistics of Functional Data

Shang

2014

Communications in Statistics - Simulation and Computation

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Re-sampling methods for estimating the distribution of descriptive statistics of functional data are considered. Through Monte-Carlo simulations, we compare the performance of several re-sampling methods commonly used for estimating the distribution of descriptive statistics.We introduce two re-sampling methods that rely on functional principal component analysis, where the scores were randomly drawn from multivariate normal distribution and Stiefel manifold. Illustrated by one-dimensional Canadian weather station data and two-dimensional bone shape data, the re-sampling methods provide a way of visualizing the distribution of descriptive statistics for functional data.

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Section: Resultsmentioning

confidence: 99%

Resampling Techniques for Estimating the Distribution of Descriptive Statistics of Functional Data

Shang

2014

Communications in Statistics - Simulation and Computation

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“…The precise result is given by the following theorem and is a generalization of Baxter's inequality, cf. p (p) given by (8) and the autoregressive coefficients given by (6). Then, there exist n 0 ∈ N and C < ∞, both not depending on n, such that…”

Section: Resultsmentioning

confidence: 99%

“…Comparing the first p rows of this system with (8) it is obvious that the right-hand sides are identical which yields…”

Section: Lemma 22 Let ν Be a Norm Function As Defined In Assumptionmentioning

confidence: 99%

“…As another example, consider a practitioner that wants to resample a given time series of length n. There are many bootstrap methods available in the literature; see the review by [8]. In each of these methods, notably, the resampling mechanism is done via a probability measure that depends on n; hence, the bootstrap time series represents the nth row of a triangular array.…”

Section: Introductionmentioning

confidence: 99%

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Baxter’s inequality for triangular arrays

Meyer

McMurry²,

Politis³

2015

Math. Meth. Stat.

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A central problem in time series analysis is prediction of a future observation. The theory of optimal linear prediction has been well understood since the seminal work of A. Kolmogorov and N. Wiener during World War II. A simplifying assumption is to assume that one-step-ahead prediction is carried out based on observing the infinite past of the time series. In practice, however, only a finite stretch of the recent past is observed. In this context, Baxter's inequality is a fundamental tool for understanding how the coefficients in the finite-past predictor relate to those based on the infinite past. We prove a generalization of Baxter's inequality for triangular arrays of stationary random variables under the condition that the spectral density functions associated with the different rows converge. The motivating examples are statistical time series settings where the autoregressive coefficients are re-estimated as new data are acquired, producing new fitted processes -and new predictors -for each n.

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“…The bootstrap method is a re-sampling method for the confidence intervals ( [11]). In the present section the confidence limits based on the parametric bootstrap method are obtained for the parameters under study.…”

Section: Bootstrap Confidence Limitsmentioning

confidence: 99%

Bound lengths based on constant-stress PALT under different censoring patterns

Prakash

Singh

2017

Int. J. Sci. World

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The Gompertz distribution is assumed in the present article for drawing the inferences based on Bayesian methodology. Constant-Stress Partially Accelerated Life Test (CS-PALT) have used for the underlying distribution on first-failure Progressive (FFP) censoring scheme. All special cases of the FFP censoring scheme have used for the present comparative analysis. The comparison has been done between different special cases of FFP based on Approximate Confidence Lengths (ACL) under Normal approximation, Bootstrap Confidence Length (BCL) and One-Sample Bayes Prediction Bound Lengths (BPBL). A simulation study have been carried out for the present analysis.

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Bootstrap methods for dependent data: A review

Cited by 95 publications

References 87 publications

Resampling Techniques for Estimating the Distribution of Descriptive Statistics of Functional Data

Resampling Techniques for Estimating the Distribution of Descriptive Statistics of Functional Data

Baxter’s inequality for triangular arrays

Bound lengths based on constant-stress PALT under different censoring patterns

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