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Russell Davidson - One of the best experts on this subject based on the ideXlab platform.
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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.
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Diagnostics for the Bootstrap and fast double Bootstrap
Econometric 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.
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The Iterated Bootstrap
SSRN 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.
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the wild Bootstrap tamed at last
Post-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.
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Improving the reliability of Bootstrap tests with the fast double Bootstrap
Computational Statistics & Data Analysis, 2007Co-Authors: Russell Davidson, James G. MackinnonAbstract:Two procedures are proposed for estimating the rejection probabilities (RPs) of Bootstrap tests in Monte Carlo experiments without actually computing a Bootstrap test for each replication. These procedures are only about twice as expensive (per replication) as estimating RPs for asymptotic tests. Then a new procedure is proposed for computing Bootstrap P values that will often be more accurate than ordinary ones. This ''fast double Bootstrap'' (FDB) is closely related to the double Bootstrap, but it is far less computationally demanding. Simulation results for three different cases suggest that the FDB can be very useful in practice.
Abdelhak M. Zoubir - One of the best experts on this subject based on the ideXlab platform.
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Robust Bootstrap methods with an application to geolocation in harsh LOS/NLOS environments
2014 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.
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Robust Bootstrap based observation classification for Kalman Filtering in harsh LOS/NLOS environments
2014 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.
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Bootstrap Methods and Applications
IEEE 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.
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The Bootstrap and tolerance regions
Conference Record of the Thirty-Third Asilomar Conference on Signals Systems and Computers (Cat. No.CH37020), 1999Co-Authors: Abdelhak M. Zoubir, R.f. Brcich, D.w. Tufts, E.c. RealAbstract:We present results for Bootstrap detection procedures that make use of tolerance regions. The Bootstrap matched-filter and the CFAR Bootstrap matched filter are designed so that with a given probability the level of the test is not exceeded. Simulation results show that the actual false alarm rate is consistently lower than that of the Bootstrap matched filter. Real data experiments are also presented. They demonstrate the power of Bootstrap and tolerance region principles in signal detection.
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the Bootstrap and its application in signal processing
IEEE Signal Processing Magazine, 1998Co-Authors: Abdelhak M. Zoubir, B BoashashAbstract:The Bootstrap is an attractive tool for assessing the accuracy of estimators and testing hypothesis for parameters where conventional techniques are not valid, such as in small data-sample situations. We highlight the motivations for using the Bootstrap in typical signal processing applications and give several practical examples. Bootstrap methods for testing statistical hypotheses are described and we provide an analysis of the accuracy of Bootstrap tests. We also discuss how the Bootstrap can be used to estimate a variance-stabilizing transformation to define a pivotal statistic, and we demonstrate the use of the Bootstrap for constructing confidence intervals for flight parameters in a passive acoustic emission problem.
Emmanuel Flachaire - One of the best experts on this subject based on the ideXlab platform.
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the wild Bootstrap tamed at last
Post-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.
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Bootstrapping heteroskedastic regression models: wild Bootstrap vs. pairs Bootstrap
Computational 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.
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the wild Bootstrap tamed at last
LSE 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.
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the wild Bootstrap tamed at last
Econometric Society World Congress 2000 Contributed Papers, 2000Co-Authors: Russell Davidson, Emmanuel FlachaireAbstract:In this paper we are interested in inference based on heteroskedasticity consistent covariance matrix estimators, for which the appropriate Bootstrap is a version of the wild Bootstrap. Simulation results, obtained by a new very efficient method, show that all wild Bootstrap tests exhibit substantial size distortion if the error terms are skewed and strongly heteroskedastic. The distortion is however less, sometimes much less, if one uses a version of the wild Bootstrap, belonging to a class we call ``tamed'', which benefit from an asymptotic refinement related to the asymptotic independence of the Bootstrapped test statistic and the Bootstrap DGP. This version always gives better results than the version usually recommended in the literature, and gives exact results for some specific cases. However, when exact results are not available, we find that the rate of convergence to zero of the size distortion of wild Bootstrap tests is not very rapid: in some cases, significant size distortion still remains for samples of size~100.
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the wild Bootstrap tamed at last
G.R.E.Q.A.M., 1999Co-Authors: Russell Davidson, Emmanuel FlachaireAbstract:In this paper we are interested in inference based on heteroskedasticity consistent covariance matrix estimators, for which the appropriate Bootstrap is a version of the wild Bootstrap. Simulation results, obtained by a new very efficient methos, show that all wild Bootstraps tests exhibit substantial size distortion if the error terms are skewed and strongly heteroskedastic.
Michael I. Jordan - One of the best experts on this subject based on the ideXlab platform.
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a scalable Bootstrap for massive data
Journal of The Royal Statistical Society Series B-statistical Methodology, 2014Co-Authors: Ariel Kleiner, Ameet Talwalkar, Purnamrita Sarkar, Michael I. JordanAbstract:type="main" xml:id="rssb12050-abs-0001"> The Bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large data sets—which are increasingly prevalent—the calculation of Bootstrap-based quantities can be prohibitively demanding computationally. Although variants such as subsampling and the m out of n Bootstrap can be used in principle to reduce the cost of Bootstrap computations, these methods are generally not robust to specification of tuning parameters (such as the number of subsampled data points), and they often require knowledge of the estimator's convergence rate, in contrast with the Bootstrap. As an alternative, we introduce the ‘bag of little Bootstraps’ (BLB), which is a new procedure which incorporates features of both the Bootstrap and subsampling to yield a robust, computationally efficient means of assessing the quality of estimators. The BLB is well suited to modern parallel and distributed computing architectures and furthermore retains the generic applicability and statistical efficiency of the Bootstrap. We demonstrate the BLB's favourable statistical performance via a theoretical analysis elucidating the procedure's properties, as well as a simulation study comparing the BLB with the Bootstrap, the m out of n Bootstrap and subsampling. In addition, we present results from a large-scale distributed implementation of the BLB demonstrating its computational superiority on massive data, a method for adaptively selecting the BLB's tuning parameters, an empirical study applying the BLB to several real data sets and an extension of the BLB to time series data.
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The Big Data Bootstrap
ICML, 2012Co-Authors: Ariel Kleiner, Michael I. JordanAbstract:The Bootstrap provides a simple and pow- erful means of assessing the quality of esti- mators. However, in settings involving large datasets, the computation of Bootstrap-based quantities can be prohibitively demanding. As an alternative, we present the Bag of Little Bootstraps (BLB), a new procedure which incorporates features of both the Bootstrap and subsampling to obtain a robust, compu- tationally efficient means of assessing estima- tor quality. BLB is well suited to modern par- allel and distributed computing architectures and retains the generic applicability, statisti- cal efficiency, and favorable theoretical prop- erties of the Bootstrap. We provide the re- sults of an extensive empirical and theoretical investigation of BLB’s behavior, including a study of its statistical correctness, its large- scale implementation and performance, selec- tion of hyperparameters, and performance on real data. 1.
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a scalable Bootstrap for massive data
arXiv: Methodology, 2011Co-Authors: Ariel Kleiner, Ameet Talwalkar, Purnamrita Sarkar, Michael I. JordanAbstract:The Bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large datasets---which are increasingly prevalent---the computation of Bootstrap-based quantities can be prohibitively demanding computationally. While variants such as subsampling and the $m$ out of $n$ Bootstrap can be used in principle to reduce the cost of Bootstrap computations, we find that these methods are generally not robust to specification of hyperparameters (such as the number of subsampled data points), and they often require use of more prior information (such as rates of convergence of estimators) than the Bootstrap. As an alternative, we introduce the Bag of Little Bootstraps (BLB), a new procedure which incorporates features of both the Bootstrap and subsampling to yield a robust, computationally efficient means of assessing the quality of estimators. BLB is well suited to modern parallel and distributed computing architectures and furthermore retains the generic applicability and statistical efficiency of the Bootstrap. We demonstrate BLB's favorable statistical performance via a theoretical analysis elucidating the procedure's properties, as well as a simulation study comparing BLB to the Bootstrap, the $m$ out of $n$ Bootstrap, and subsampling. In addition, we present results from a large-scale distributed implementation of BLB demonstrating its computational superiority on massive data, a method for adaptively selecting BLB's hyperparameters, an empirical study applying BLB to several real datasets, and an extension of BLB to time series data.
Mark S. Springer - One of the best experts on this subject based on the ideXlab platform.
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Gene-wise resampling outperforms site-wise resampling in phylogenetic coalescence analyses
Molecular Phylogenetics and Evolution, 2018Co-Authors: Mark P. Simmons, Daniel B Sloan, Mark S. Springer, John GatesyAbstract:Abstract In summary (“two-step”) coalescent analyses of empirical data, researchers typically apply the Bootstrap to quantify branch support for clades inferred on the optimal species tree. We tested whether site-wise Bootstrap analyses provide consistently more conservative support than gene-wise Bootstrap analyses. We did so using data from three empirical phylogenomic studies and employed four coalescent methods (ASTRAL, MP-EST, NJst, and STAR). We demonstrate that application of site-wise Bootstrapping generally resulted in gene-trees with substantial additional conflicts relative to the original data and this approach therefore cannot be relied upon to provide conservative support. Instead the site-wise Bootstrap can provide high support for apparently incorrect clades. We provide a script ( https://github.com/dbsloan/msc_tree_resampling ) that implements gene-wise resampling, using either the Bootstrap or the jackknife, for use with ASTRAL, MP-EST, NJst, and STAR. We demonstrate that the gene-wise Bootstrap outperformed the site-wise Bootstrap for the primary focal clades for all four coalescent methods that were applied to all three empirical studies. For summary coalescent analyses we suggest that gene-wise resampling support should be favored over gene + site or site-wise resampling when numerous genes are sampled because site-wise resampling causes substantially greater gene-tree-estimation error.
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An Analysis of Marsupial Interordinal Relationships Based on 12S rRNA, tRNA Valine, 16S rRNA, and Cytochrome b Sequences
Journal of Mammalian Evolution, 1999Co-Authors: Angela Burk, Michael Westerman, John R. Kavanagh, Mark S. SpringerAbstract:The basal split among living marsupials is traditionally placed between the cohorts Ameridelphiaand Australidelphia. Ameridelphia includes all American forms excepting the South American Dramicuipx gliroidex (Order Microbiotheria). Australidelphia includes all Australasian taxaplus Dromiciops glinmles . DNA data support Eometatheria Dromiciaps + Diprotodontia +Dasyuromorphia + Notoryctemorphia) but do not resolve the position of bandicoots, whetherwith other australidelphians or with ameridelphians. Also, the most robust molecular trees (DNAhybridization, multigene studies) exhibit minimal branch subdivision and raise the possibility ofartit'actual associations owing to long branch attraction. We analyzed data sets that consistedof complete sequences tor four niitochondrial genes (cytochrome b , 12S rRNA, tRNA valine,16S rRNA). One data set included 14 marsupial taxa. A second data set included 14 marsupialsas well as outgroup sequences (one monolreme; 20 placentals). Phylogenetic analyses includedparsimony, minimum evolution, maximum likelihood, and quartet puzzling. When phylogeneticanalyses were restricted to just the marsupial sequences, there was 75 to 96% boostrap supportfor the separation of Ameridelphia versus Australidelphia. This suggests that either one orboth of these groups are monophyletic. Also, there was 71 to 98% Bootstrap support for theseparation of Eometatheria versus Ameridelphia + Peramelina. Nonmonophyly of several a prioriclades was accepted by at least some statistical tests including the following: Diprotodontia+ Peramelina, Notoryctemorphia + Peramelina, Diprotodonlia + Notoryctemorphia, and themonophyly of Australasian marsupials. With the inclusion of outgroup sequences, there wasreduced Bootstrap support for associations among marsupial orders and statistical tests failed toreject all interordinal associations that were tested.