Dependent Lindeberg central limit theorem and some applications

Bardet, Jean-Marc; Doukhan, Paul; Lang, Gabriel; Ragache, Nicolas

doi:10.1051/ps:2007053

Cited by 46 publications

(67 citation statements)

References 14 publications

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“…Therefore we present an alternative route to establishing subsampling consistency, by considering the θ-weak dependence literature of Doukhan and Louhichi (1999) and Bardet et al (2008). By combining the proofs of Theorem 11.3.1 of Politis et al (1999) and Lemma 3.1 of Ango-Nze et al (2003) it is possible to establish the desired consistency rate under assumptions typical to the literature; for completeness we present the result in Appendix B with proof.…”

Section: Subsamplingmentioning

confidence: 99%

“…By combining the proofs of Theorem 11.3.1 of Politis et al (1999) and Lemma 3.1 of Ango-Nze et al (2003) it is possible to establish the desired consistency rate under assumptions typical to the literature; for completeness we present the result in Appendix B with proof. The application of Theorem 4 to the problem of our paper is immediate, using Theorem 3 to identify Z as σ t is positive -to ensure λ-and θ-weak dependence (see Doukhan and Louhichi (1999) and Bardet et al (2008) for definitions). The validity of subsampling under weak dependence is proved in Appendix B under a condition of polynomial decay of the weak dependence coefficients r .…”

Section: Subsamplingmentioning

confidence: 99%

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Subsampling inference for the mean of heavy‐tailed long‐memory time series

Jach

McElroy

Politis

2011

Journal Time Series Analysis

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In this paper we revisit a time series model introduced by McElroy and Politis (2007a) and generalize it in several ways to encompass a wider class of stationary, nonlinear, heavy-tailed time series with long memory. The joint asymptotic distribution for the sample mean and sample variance under the extended model is derived; the associated convergence rates are found to depend crucially on the tail thickness and long memory parameter. A self-normalized sample mean, that concurrently captures the tail and memory behavior, is defined. Its asymptotic distribution is approximated by subsampling without the knowledge of tail or/and memory parameters; a result of independent interest regarding subsampling consistency for certain long-range dependent processes is provided. The subsampling-based confidence intervals for the process mean are shown to have good empirical coverage rates in a simulation study. The influence of block size on the coverage and the performance of a data-driven rule for block size selection are assessed. The methodology is further applied to the series of packet-counts from Ethernet traffic traces.

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Section: Subsamplingmentioning

confidence: 99%

Section: Subsamplingmentioning

confidence: 99%

Subsampling inference for the mean of heavy‐tailed long‐memory time series

Jach

McElroy

Politis

2011

Journal Time Series Analysis

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“…To obtain decent performance over a range of data processes, either the Parzen or a trapezoidal taper is recommended. 4 While the MAC approach of Robinson (2005) is also applicable, we omit to study it here because it is not based upon self-normalization, which is the focus of our paper. In summary, we provide a viable framework for conducting inference for the mean, supplying a unified asymptotic theory that covers all different types of memory under a single umbrella.…”

Section: Discussionmentioning

confidence: 99%

Distribution theory for the studentized mean for long, short, and negative memory time series

McElroy

Politis

2013

Journal of Econometrics

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We consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory, short memory, negative/intermediate memory, or is the firstdifference of such a process. The rate of growth of this variance depends crucially on the type of memory, and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically. We also present asymptotic results for the case that the bandwidth is a fixed proportion of sample size, extending known results to the case of flat-top tapers. We adopt the fixed proportion bandwidth perspective in our empirical section, presenting two methods for estimating the limiting critical values -both the subsampling method and a plug-in approach. Simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean. Both methods perform wellalthough the subsampling method appears to be better sized -and provide a viable framework for conducting inference for the mean. In summary, we supply a unified asymptotic theory that covers all different types of memory under a single umbrella.

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“…Concluding remark. It is well known in the literature that processes satisfying some mixing properties have interesting statistical properties (see [16,17,18,20,3,27,34,38] and many others) such as moment inequalities, central limit theorem ... The mixing properties satisfied by our models, namely (η u,v )-mixing properties, are not standard ones and some more work is needed to get these statistical properties.…”

Section: 23mentioning

confidence: 99%

Some mixing properties of conditionally independent processes

Kacem

Loisel

Maume-Deschamps

2016

Communications in Statistics - Theory and Methods

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Abstract. In this paper we consider conditionally independent processes with respect to some dynamic factor. More precisely, we assume that for all i ∈ N, the random variables X1, . . . , Xi are conditionally independent with respect to vector V i = (V1, . . . , Vi). We study the mixing properties of the Xi's when conditioning is given with respect to unbounded memory of the factor. Our work is motivated by some real examples related to risk theory.Acknowledgments.

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Dependent Lindeberg central limit theorem and some applications

Cited by 46 publications

References 14 publications

Subsampling inference for the mean of heavy‐tailed long‐memory time series

Subsampling inference for the mean of heavy‐tailed long‐memory time series

Distribution theory for the studentized mean for long, short, and negative memory time series

Some mixing properties of conditionally independent processes

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