Validity of Blockwise Bootstrap for Empirical Processes with Stationary Observations

Naik‐Nimbalkar, U. V.; Rajarshi, M. B.

doi:10.1214/aos/1176325507

Cited by 48 publications

(35 citation statements)

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“…, ∈ IR m }, where m 1, under the condition that the block length l(n) = O(n 1/2− ) with > 0, Bühlmann (1994) proves that the bootstrapped vector empirical process converges weakly almost surely to the same Gaussian process to which the original empirical process converges. Naik-Nimbalkar and Rajarshi (1994) give similar results for a sequence of random variables (i.e., for m = 1). They establish almost-sure weak convergence assuming l(n) = O(n 1/2− ) for 1/4 < < 1/2, and only convergence in probability if l(n) = O(n 1/2− ) for 0 < 1/4.…”

Section: Weak Convergence Of Bootstrapped Empirical Processessupporting

confidence: 57%

Bootstrapping the Empirical Distribution Function of a Spatial Process

Zhu

Lahiri

2007

Stat Infer Stoch Process

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Section: Weak Convergence Of Bootstrapped Empirical Processessupporting

confidence: 57%

Bootstrapping the Empirical Distribution Function of a Spatial Process

Zhu

Lahiri

2007

Stat Infer Stoch Process

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“…may be dependent. We focus on the so-called circular bootstrap [44,45], which is only a slight modification of the moving blocks bootstrap [15,37,39,41]. To ensure that in the following F * n is the distribution function of a probability measure, we assume that n ranges only over N m := {m k : k = 1, 2, .…”

Section: Bootstrap Consistencymentioning

confidence: 99%

Statistical Inference for Expectile‐based Risk Measures

Krätschmer

Zähle

2017

Scandinavian J Statistics

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Expectiles were introduced by Newey and Powell [43] in the context of linear regression models. Recently, Bellini et al. [6] revealed that expectiles can also be seen as reasonable law-invariant risk measures. In this article, we show that the corresponding statistical functionals are continuous w.r.t. the 1-weak topology and suitably functionally differentiable. By means of these regularity results we can derive several properties such as consistency, asymptotic normality, bootstrap consistency, and qualitative robustness of the corresponding estimators in nonparametric and parametric statistical models.

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“…Since its introduction several papers have been written which show and extend its validity, see e.g. B uhlmann (1994a, 1995), B uhlmann and K unsch (1995), G otze and K unsch (1993), Naik-Nimbalkar and Rajarshi (1994), Politis and Romano (1992, 1993.…”

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confidence: 99%

Block length selection in the bootstrap for time series

Bühlmann

Künsch

1999

Computational Statistics & Data Analysis

111

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The blockwise bootstrap is a modi cation of Efron's bootstrap designed to give correct results for dependent stationary observations. One drawback o f the method is that it depends critically on a block length which so far had to be chosen by the user. Here we propose a data-driven method to select this block length. It is based on the equivalence of the blockwise bootstrap variance to a lag weight estimator of a spectral density at the origin. The relevant spectral density is the one of the process given by the in uence function of the statistic to be bootstrapped. In this equivalence the block l e n g t h i s t h e inverse of the bandwidth. We t h us apply a recently developed local bandwidth selection procedure to the time series given by the estimated in uence function. The lag window corresponding to the blockwise bootstrap is the triangular or Bartlett window. In order to obtain other windows we i n troduce a correlated weights bootstrap where observations are weighted by an MA-process. The correlations of the weight process correspond to the lag weights.

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Validity of Blockwise Bootstrap for Empirical Processes with Stationary Observations

Cited by 48 publications

References 0 publications

Bootstrapping the Empirical Distribution Function of a Spatial Process

Bootstrapping the Empirical Distribution Function of a Spatial Process

Statistical Inference for Expectile‐based Risk Measures

Block length selection in the bootstrap for time series

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