Dependent Wild Bootstrap for the Empirical Process

Doukhan, Paul; Lang, Gabriel; Leucht, Anne; Neumann, Michael H.

doi:10.1111/jtsa.12106

Cited by 23 publications

(20 citation statements)

References 21 publications

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“…Recently, showed the consistency of the dependent multiplier bootstrap for U-statistics and also established the validity of dependent multiplier bootstrap procedures for change-point test statistics based on this class of statistics. For quantiles, the block bootstrap was investigated by Sun and Lahiri (2006) and the multiplier bootstrap by Doukhan et al (2015). For U-quantiles, such as the Q α n , we are unaware of any work concerning bootstrap methods.…”

Section: Discussionmentioning

confidence: 99%

Tests for Scale Changes Based on Pairwise Differences

Gerstenberger

Vogel

Wendler

2019

Journal of the American Statistical Association

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In many applications it is important to know whether the amount of fluctuation in a series of observations changes over time. In this article, we investigate different tests for detecting change in the scale of mean-stationary time series. The classical approach based on the CUSUM test applied to the squared centered, is very vulnerable to outliers and impractical for heavy-tailed data, which leads us to contemplate test statistics based on alternative, less outlier-sensitive scale estimators.It turns out that the tests based on Gini's mean difference (the average of all pairwise distances) or generalized Qn estimators (sample quantiles of all pairwise distances) are very suitable candidates. They improve upon the classical test not only under heavy tails or in the presence of outliers, but also under normality. An explanation for this counterintuitive result is that the corresponding long-run variance estimates are less affected by a scale change than in the case of the sample-variance-based test.We use recent results on the process convergence of U-statistics and U-quantiles for dependent sequences to derive the limiting distribution of the test statistics and propose estimators for the long-run variance. We perform a simulations study to investigate the finite sample behavior of the test and their power. Furthermore, we demonstrate the applicability of the new change-point detection methods at two real-life data examples from hydrology and finance.

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Section: Discussionmentioning

confidence: 99%

Tests for Scale Changes Based on Pairwise Differences

Gerstenberger

Vogel

Wendler

2019

Journal of the American Statistical Association

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“…, that is, the LDWB implicitly corrects for the asymptotic bias in the empirical CDF. Second, time series dependence in X (j−1)kn+i plays a different role in our setting compared with in Shao (2010) and Doukhan et al (2015). Whereas they seek to replicate a lead-lag covariance structure of the observations, needing a condition of the form Cov(v * s , v * r ) → 1 as n → ∞, dependence in the present setting is created by the unwarranted estimation errors in V n,j , which are perfectly dependent within a given block j = 1, .…”

Section: The Local Dependent Wild Bootstrap For the Empirical Cdfmentioning

confidence: 94%

“…The random increments and empirical CDF in (12) and (13), respectively, illustrate the differences between the present bootstrap setting and the corresponding in Doukhan et al (2015), who also consider DWB inference for empirical processes. In our case, the problem is more challenging due to the distributional properties of (3) may differ at coarse and fine time scales, depending on S t and Y t , which necessitates an infill asymptotic approach to estimation and the identification of the locally dominant stochastic component, S t .…”

Section: The Local Dependent Wild Bootstrap For the Empirical Cdfmentioning

confidence: 97%

“…The framework in Section 2 presents several challenges that are unprecedented in the bootstrap literature, e.g., the combination of the general class processes in (3), the infill asymptotic setting and the need for replication of higher-order central limit theory. To overcome such challenges, we design a new and general resampling procedure -the locally dependent wild bootstrap (LDWB) -which is inspired by the dependent wild bootstraps (DWBs) in Shao (2010) and Doukhan et al (2015), but, as will be detailed below, differs in subtle, yet important ways, to remain valid in the present setting.…”

Section: The Local Dependent Wild Bootstrap For the Empirical Cdfmentioning

confidence: 99%

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Inference for local distributions at high sampling frequencies: A bootstrap approach

Hounyo

Varneskov

2020

Journal of Econometrics

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We study inference for the local innovations of Itô semimartingales. Specifically, we construct a resampling procedure for the empirical CDF of high-frequency innovations that have been standardized using a nonparametric estimate of its stochastic scale (volatility) and truncated to rid the effect of "large" jumps. Our locally dependent wild bootstrap (LDWB) accommodate issues related to the stochastic scale and jumps as well as account for a special block-wise dependence structure induced by sampling errors. We show that the LDWB replicates first and second-order limit theory from the usual empirical process and the stochastic scale estimate, respectively, as well as an asymptotic bias. Moreover, we design the LDWB sufficiently general to establish asymptotic equivalence between it and and a nonparametric local block bootstrap, also introduced here, up to second-order distribution theory. Finally, we introduce LDWB-aided Kolmogorov-Smirnov tests for local Gaussianity as well as local von-Mises statistics, with and without bootstrap inference, and establish their asymptotic validity using the second-order distribution theory. The finite sample performance of CLT and LDWB-aided local Gaussianity tests are assessed in a simulation study as well as two empirical applications. Whereas the CLT test is oversized, even in large samples, the size of the LDWB tests are accurate, even in small samples. The empirical analysis verifies this pattern, in addition to providing new insights about the distributional properties of equity indices, commodities, exchange rates and popular macro finance variables.

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“…Forμ =F n , the empirical size is much larger than the nominal one for all choices of a and q. The over-rejection under the null hypothesis seems to be typical for bootstrap methods (see [19]). Conversely, under the alternative, the empirical power decreases with rising bandwidth q, but the effect is more pronounced forμ = F n than forμ =F n (see, e.g., Tables 3 and 4).…”

Section: Simulation Studymentioning

confidence: 97%

Change-point detection and bootstrap for Hilbert space valued random fields

Bucchia

Wendler

2017

Journal of Multivariate Analysis

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The problem of testing for the presence of epidemic changes in random fields is investigated. In order to be able to deal with general changes in the marginal distribution, a Cramér-von Mises type test is introduced which is based on Hilbert space theory. A functional central limit theorem for ρ-mixing Hilbert space valued random fields is proven. In order to avoid the estimation of the long-run variance and obtain critical values, Shao's dependent wild bootstrap method is adapted to this context. For this, a joint functional central limit theorem for the original and the bootstrap sample is shown. Finally, the theoretic results are supplemented by a short simulation study.

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Dependent Wild Bootstrap for the Empirical Process

Cited by 23 publications

References 21 publications

Tests for Scale Changes Based on Pairwise Differences

Tests for Scale Changes Based on Pairwise Differences

Inference for local distributions at high sampling frequencies: A bootstrap approach

Change-point detection and bootstrap for Hilbert space valued random fields

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