Tapered block bootstrap

Paparoditis, Efstathios; Politis, Dimitris N.

doi:10.1093/biomet/88.4.1105

Cited by 119 publications

(132 citation statements)

References 29 publications

Supporting

Mentioning

130

Contrasting

Order By: Relevance

“…Related results are presented in Bühlmann ([15], Lemmas 3.12 and 3.13) and Shao ([44], Proposition 2.1) for the dependent multiplier bootstrap when the statistic of interest is the sample mean. The aim of this section is to extend the aforementioned results to the dependent multiplier bootstrap for C n and propose an estimator of ℓ n in the spirit of those investigated in Paparoditis and Politis [33], Politis and White [38] and Patton, Politis and White [34] for other resampling schemes. Since the dependent multiplier bootstrap for C n is based on the corresponding bootstrap approximation for B n , we propose to base our estimator of the bandwidth parameter on the accuracy of the latter technique.…”

Section: Estimation Of the Bandwidth Parameter ℓ Nmentioning

confidence: 99%

“…The above estimator depends on the choice of the integer L appearing in (5.6). To estimate L, we suggest proceeding along the lines of Politis and White ( [38], Section 3.2) (see also Paparoditis and Politis [33], page 1112). Letρ j (k), j ∈ {1, .…”

Section: Estimation Of the Bandwidth Parameter ℓ Nmentioning

confidence: 99%

“…Their graphs are represented in Figure 1. The flat top (or trapezoidal) kernel, parametrized by c ∈ [0, 1], was used in Paparoditis and Politis [33] in the context of the tapered block bootstrap for the mean. These authors found that, within the class of trapezoidal kernels symmetric around 0.5 and with support (0, 1), κ F,0.14 , rescaled and shifted to have support (0, 1), minimizes the asymptotic mean squared error of the bootstrapping procedure.…”

Section: The Moving Average Approachmentioning

confidence: 99%

See 2 more Smart Citations

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

Bücher¹,

Kojadinovic²

2016

Bernoulli

View full text Add to dashboard Cite

Two key ingredients to carry out inference on the copula of multivariate observations are the empirical copula process and an appropriate resampling scheme for the latter. Among the existing techniques used for i.i.d. observations, the multiplier bootstrap of Rémillard and Scaillet (J. Multivariate Anal. 100 (2009) 377-386) frequently appears to lead to inference procedures with the best finite-sample properties. Bücher and Ruppert (J. Multivariate Anal. 116 (2013) 208-229) recently proposed an extension of this technique to strictly stationary strongly mixing observations by adapting the dependent multiplier bootstrap of Bühlmann (The blockwise bootstrap in time series and empirical processes (1993) ETH Zürich, Section 3.3) to the empirical copula process. The main contribution of this work is a generalization of the multiplier resampling scheme proposed by Bücher and Ruppert along two directions. First, the resampling scheme is now genuinely sequential, thereby allowing to transpose to the strongly mixing setting many of the existing multiplier tests on the unknown copula, including nonparametric tests for change-point detection. Second, the resampling scheme is now fully automatic as a data-adaptive procedure is proposed which can be used to estimate the bandwidth parameter. A simulation study is used to investigate the finite-sample performance of the resampling scheme and provides suggestions on how to choose several additional parameters. As by-products of this work, the validity of a sequential version of the dependent multiplier bootstrap for empirical processes of Bühlmann is obtained under weaker conditions on the strong mixing coefficients and the multipliers, and the weak convergence of the sequential empirical copula process is established under many serial dependence conditions. Keywords: lag window estimator; multiplier central limit theorem; multivariate observations; partial-sum process; ranks; serial dependence This is an electronic reprint of the original article published by the ISI/BS in Bernoulli, 2016, Vol. 22, No. 2, 927-968. This reprint differs from the original in pagination and typographic detail.

show abstract

Section: Estimation Of the Bandwidth Parameter ℓ Nmentioning

confidence: 99%

Section: Estimation Of the Bandwidth Parameter ℓ Nmentioning

confidence: 99%

Section: The Moving Average Approachmentioning

confidence: 99%

See 1 more Smart Citation

A dependent multiplier bootstrap for the sequential empirical copula process under strong mixing

Bücher¹,

Kojadinovic²

2016

Bernoulli

View full text Add to dashboard Cite

show abstract

“…multiplier approach of the previous section would not work in this setting since it cannot take care of the serial dependence features of the time series. Therefore we make use of a refinement of this technique, called the tapered block multiplier bootstrap, which has been recently proposed by Bücher and Ruppert (2012) and which is based on earlier work by Bühlmann (1993) and Paparoditis and Politis (2001). Analogously to the i.i.d.…”

Section: Critical Values For τ N For Serial Dependent Datamentioning

confidence: 99%

Nonparametric tests for tail monotonicity

Berghaus

Bücher

2014

Journal of Econometrics

View full text Add to dashboard Cite

This article proposes nonparametric tests for tail monotonicity of bivariate random vectors. The test statistic is based on a Kolmogorov-Smirnov-type functional of the empirical copula. Depending on the serial dependence features of the data, we propose two multiplier bootstrap techniques to approximate the critical values. We show that the test is able to detect local alternatives converging to the null hypothesis at rate n −1/2 with a non-trivial power. A simulation study is performed to investigate the finite-sample performance and finally the procedure is illustrated by testing intergenerational income mobility.

show abstract

“…Here the index t of the first observation in the block is drawn from the discrete uniform distribution on 1, .., t, whereas m is sampled from the geometric distribution such that: P(m = g) = (1 − p) g−1 p; g = 1, 2, ... and p ∈ (0, 1). Finally, in order to deal with the boundaries effects between neighbored blocks, ad hoc procedures (tapering) have been studied ( [30], [31]). The scheme adopted in this paper is the Stationary Bootstrap (henceforth SB).…”

Section: The Employed Bootstrap Schemementioning

confidence: 99%