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Russell Davidson – 1st expert on this subject based on the ideXlab platform
Improvements in Bootstrap Inference, 2018Co-Authors: Russell Davidson, Andrea MonticiniAbstract:
The fast double Bootstrap can improve considerably on the single Bootstrap when the Bootstrapped statistic is approximately independent of the Bootstrap DGP. This is because, among the approximations that underlie the fast double Bootstrap (FDB), is the assumption of such independence. In this paper, use is made of a discrete formu- lation of Bootstrapping in order to develop a conditional version of the FDB, which makes use of the joint distribution of a statistic and its Bootstrap counterpart, rather than the joint distribution of the statistic and the full distribution of its Bootstrap counterpart, which is available only by means of a simulation as costly as the full double Bootstrap. Simulation evidence shows that the conditional FDB can greatly improve on the performance of the FDB when the statistic and the Bootstrap DGP are far from independent, while giving similar results in cases of near independence.
Diagnostics for the Bootstrap and fast double BootstrapEconometric Reviews, 2017Co-Authors: Russell DavidsonAbstract:
The Bootstrap is typically less reliable in the context of time-series models with serial correlation of unknown form than when regularity conditions for the conventional IID Bootstrap apply. It is, therefore, useful to have diagnostic techniques capable of evaluating Bootstrap performance in specific cases. Those suggested in this paper are closely related to the fast double Bootstrap (FDB) and are not computationally intensive. They can also be used to gauge the performance of the FDB itself. Examples of Bootstrapping time series are presented, which illustrate the diagnostic procedures, and show how the results can cast light on Bootstrap performance.
The Iterated BootstrapSSRN Electronic Journal, 2011Co-Authors: Russell Davidson, Mirza TrokicAbstract:
The standard forms of Bootstrap iteration are very computationally demanding. As a result, there have been several attempts to alleviate the computational burden by use of approximations. In this paper, we extend the fast double Bootstrap of Davidson and MacKinnon (2007) to higher orders of iteration, and provide algorithms for their implementation. The new methods make computational demands that increase only linearly with the level of iteration, unlike standard procedures, whose demands increase exponentially. In a series of simulation experiments, we show that the fast triple Bootstrap improves on both the standard and fast double Bootstraps, in the sense that it suers from less size distortion under the null with no accompanying loss of power.
Abdelhak M. Zoubir – 2nd expert on this subject based on the ideXlab platform
Robust Bootstrap methods with an application to geolocation in harsh LOS/NLOS environments2014 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2014Co-Authors: Stefan Vlaski, Michael Muma, Abdelhak M. ZoubirAbstract:
The Bootstrap is a powerful computational tool for statistical inference that allows for the estimation of the distribution of an estimate without distributional assumptions on the underlying data, reliance on asymptotic results or theoretical derivations. On the other hand, robustness properties of the Bootstrap in the presence of outliers are very poor, irrespective of the robustness of the underlying estimator. This motivates the need to robustify the Bootstrap procedure itself. Improvements to two existing robust Bootstrap methods are suggested and a novel approach for robustifying the Bootstrap is introduced. The methods are compared in a simulation study and the proposed method is applied to robust geolocation.
Robust Bootstrap based observation classification for Kalman Filtering in harsh LOS/NLOS environments2014 IEEE Workshop on Statistical Signal Processing (SSP), 2014Co-Authors: Stefan Vlaski, Abdelhak M. ZoubirAbstract:
The Bootstrap allows for the estimation of the distribution of an estimate without requiring assumptions on the distribution of the underlying data, relying on asymptotic results or theoretical derivations. In contrast to a point estimate, the distribution estimate captures the uncertainty about the statistic of interest. We introduce a novel robust Bootstrap method and demonstrate how this additional information is utilized to improve the performance of robust tracking methods. A robust Bootstrap method is crucial, because the classical Bootstrap is highly sensitive to outliers, irrespective of the robustness of the underlying estimator. Using the robust distribution estimate of the state prediction as a measure of confidence, the Bootstrap allows to incorporate an observation weighting scheme into the tracking algorithm, which enhances performance.
Bootstrap Methods and ApplicationsIEEE Signal Processing Magazine, 2007Co-Authors: Abdelhak M. Zoubir, D. Robert IskanderAbstract:
Given the wealth of literature on the topic supported by solutions to practical problems, we would expect the Bootstrap to be an off-the-shelf tool for signal processing problems as are maximum likelihood and least-squares methods. This is not the case, and we wonder why a signal processing practitioner would not resort to the Bootstrap for inferential problems. We may attribute the situation to some confusion when the engineer attempts to discover the Bootstrap paradigm in an overwhelming body of statistical literature. Our aim is to give a short tutorial of Bootstrap methods supported by real-life applications. This pragmatic approach is to serve as a practical guide rather than a comprehensive treatment, which can be found elsewhere. However, for the Bootstrap to be successful, we need to identify which resampling scheme is most appropriate.
Emmanuel Flachaire – 3rd expert on this subject based on the ideXlab platform
the wild Bootstrap tamed at lastPost-Print, 2008Co-Authors: Russell Davidson, Emmanuel FlachaireAbstract:
The wild Bootstrap is studied in the context of regression models with heteroskedastic disturbances. We show that, in one very specific case, perfect Bootstrap inference is possible, and a substantial reduction in the error in the rejection probability of a Bootstrap test is available much more generally. However, the version of the wild Bootstrap with this desirable property is without the skewness correction afforded by the currently most popular version of the wild Bootstrap. Simulation experiments show that this does not prevent the preferred version from having the smallest error in rejection probability in small and medium-sized samples.
Bootstrapping heteroskedastic regression models: wild Bootstrap vs. pairs BootstrapComputational Statistics & Data Analysis, 2005Co-Authors: Emmanuel FlachaireAbstract:
In regression models, appropriate Bootstrap methods for inference robust to heteroskedasticity of unknown form are the wild Bootstrap and the pairs Bootstrap. The finite sample performance of a heteroskedastic-robust test is investigated with Monte Carlo experiments. The simulation results suggest that one specific version of the wild Bootstrap outperforms the other versions of the wild Bootstrap and of the pairs Bootstrap. It is the only one for which the Bootstrap test always gives better results than the asymptotic test.
the wild Bootstrap tamed at lastLSE Research Online Documents on Economics, 2001Co-Authors: Russell Davidson, Emmanuel FlachaireAbstract:
Various versions of the wild Bootstrap are studied as applied to regression models with heteroskedastic errors. It is shown that some versions can be qualified as ‘tamed’, in the sense that the statistic Bootstrapped is asymptotically independent of the distribution of the wild Bootstrap DGP. This can, in one very specific case, lead to perfect Bootstrap inference, and leads to substantial reduction in the error in the rejection probability of a Bootstrap test much more generally. However, the version of the wild Bootstrap with this desirable property does not benefit from the skewness correction afforded by the most popular version of the wild Bootstrap in the literature. Edgeworth expansions and simulation experiments are used to show why this defect does not prevent the preferred version from having the smallest error in rejection probability in small and medium-sized samples. It is concluded that this preferred version should always be used in practice.