Blockwise empirical entropy tests for time series regressions

Bravo, Francesco

doi:10.1111/j.1467-9892.2005.00398.x

Cited by 21 publications

(16 citation statements)

References 29 publications

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“…For instance, Bravo (2004) shows the higher-order correctness of the bootstrap for inference based on empirical likelihood with i.i.d. data, while Bravo (2005) shows consistency of the block bootstrap for empirical entropy test in times series regressions with strongly mixing data. However, to our knowledge, there is no proof of higher-order correctness of the bootstrap for GEL in the literature yet.…”

Section: Introductionmentioning

confidence: 76%

A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data

2019

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We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which the method is valid. We show the asymptotic refinements of the proposed procedure, proving that it is higher-order correct under mild assumptions on the time series, the estimating functions, and the smoothing kernel. We illustrate the applicability and the advantages of our procedure for Generalized Empirical Likelihood estimation. As a by-product, our fast bootstrap provides higher-order correct asymptotic confidence distributions. Monte Carlo simulations on an autoregressive conditional duration model provide numerical evidence that the novel bootstrap yields higher-order accurate confidence intervals. A real-data application on dynamics of trading volume of stocks illustrates the advantage of our method over the routinely-applied first-order asymptotic theory, when the underlying distribution of the test statistic is skewed or fat-tailed.JEL classification: C12, C15, C22, C52, C58, G12.

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Section: Introductionmentioning

confidence: 76%

A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data

2019

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“…Many applications of tilting and perturbation arguments to contemporary, non‐parametric statistical problems have been developed, including those of Hall and Presnell (), Critchley et al . (), Hall and Yao (), Bravo (), Hall et al . (), Xu and Phillips () and the vast literature on empirical likelihood.…”

Section: Introductionmentioning

confidence: 99%

“…The use of tilting for assessing robustness, or the influence of particular data values, has been investigated by Hall and Presnell (1999a), Critchley and Marriott (2004), Lazar (2005) and Camponovo and Otsu (2012), among others. Many applications of tilting and perturbation arguments to contemporary, non-parametric statistical problems have been developed, including those of Hall and Presnell (1999b), Critchley et al (2001), Hall and Yao (2003), Bravo (2005), Hall et al (2009), Xu andPhillips (2011) and the vast literature on empirical likelihood.…”

Section: Introductionmentioning

confidence: 99%

A Tilting Approach to Ranking Influence

Genton

Hall

2014

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary We suggest a new approach, which is applicable for general statistics computed from random samples of univariate or vector‐valued or functional data, to assessing the influence that individual data have on the value of a statistic, and to ranking the data in terms of that influence. Our method is based on, first, perturbing the value of the statistic by ‘tilting’, or reweighting, each data value, where the total amount of tilt is constrained to be the least possible, subject to achieving a given small perturbation of the statistic, and, then, taking the ranking of the influence of data values to be that which corresponds to ranking the changes in data weights. It is shown, both theoretically and numerically, that this ranking does not depend on the size of the perturbation, provided that the perturbation is sufficiently small. That simple result leads directly to an elegant geometric interpretation of the ranks; they are the ranks of the lengths of projections of the weights onto a ‘line’ determined by the first empirical principal component function in a generalized measure of covariance. To illustrate the generality of the method we introduce and explore it in the case of functional data, where (for example) it leads to generalized boxplots. The method has the advantage of providing an interpretable ranking that depends on the statistic under consideration. For example, the ranking of data, in terms of their influence on the value of a statistic, is different for a measure of location and for a measure of scale. This is as it should be; a ranking of data in terms of their influence should depend on the manner in which the data are used. Additionally, the ranking recognizes, rather than ignores, sign, and in particular can identify left‐ and right‐hand ‘tails’ of the distribution of a random function or vector.

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“…1 processes, which has been shown to provide valid inference in various scenarios with time series (cf. [3,4,7,18,23,34]). Similarly to the i.i.d.…”

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confidence: 99%

A nonstandard empirical likelihood for time series

Nordman¹,

Bunzel²,

Lahiri³

2013

Ann. Statist.

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Standard blockwise empirical likelihood (BEL) for stationary, weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions. This aspect can be difficult and impacts coverage accuracy. As an alternative, this paper proposes a new version of BEL based on a simple, though nonstandard, data-blocking rule which uses a data block of every possible length. Consequently, the method does not involve the usual block selection issues and is also anticipated to exhibit better coverage performance. Its nonstandard blocking scheme, however, induces nonstandard asymptotics and requires a significantly different development compared to standard BEL. We establish the large-sample distribution of log-ratio statistics from the new BEL method for calibrating confidence regions for mean or smooth function parameters of time series. This limit law is not the usual chi-square one, but is distribution-free and can be reproduced through straightforward simulations. Numerical studies indicate that the proposed method generally exhibits better coverage accuracy than standard BEL.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1174 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Blockwise empirical entropy tests for time series regressions

Cited by 21 publications

References 29 publications

A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data

A Higher-Order Correct Fast Moving-Average Bootstrap for Dependent Data

A Tilting Approach to Ranking Influence

A nonstandard empirical likelihood for time series

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