Residual Bootstrap Research Articles

Uncertainty assessment of gamma-aminobutyric acid concentration of different brain regions in individual and group using residual bootstrap analysis.

The aim of this work is to quantify individual and regional differences in the relative concentration of gamma-aminobutyric acid (GABA) in human brain with in vivo magnetic resonance spectroscopy. Spectral editing Mescher-Garwood point resolved spectroscopy (MEGA-PRESS) sequence and GABA analysis toolkit (Gannet) were used to detect and quantify GABA in anterior cingulate cortex (ACC) and occipital cortex (OCC) of healthy volunteers. Residual bootstrap, a model-based statistical analysis technique, was applied to resample the fitting residuals of GABA from the Gaussian fitting model (referred to as GABA+ thereafter) in both individual and group data of ACC and OCC. The inter-subject coefficient of variation (CV) of GABA+ in OCC (20.66%) and ACC (12.55%) with residual bootstrap was lower than that of a standard Gaussian model analysis (21.58% and 16.73% for OCC and ACC, respectively). The intra-subject uncertainty and CV of OCC were lower than that of ACC in both analyses. The residual bootstrap analysis thus provides a more robust uncertainty estimation of individual and group GABA+ detection in different brain regions, which may be useful in our understanding of GABA biochemistry in brain and its use for the diagnosis of related neuropsychiatric diseases.

Probabilistic tractography using Lasso bootstrap.

Diffusion magnetic resonance imaging (dMRI) can be used for noninvasive imaging of white matter tracts. Using fiber tracking, which propagates fiber streamlines according to fiber orientations (FOs) computed from dMRI, white matter tracts can be reconstructed for investigation of brain diseases and the brain connectome. Because of image noise, probabilistic tractography has been proposed to characterize uncertainties in FO estimation. Bootstrap provides a nonparametric approach to the estimation of FO uncertainties and residual bootstrap has been used for developing probabilistic tractography. However, recently developed models have incorporated sparsity regularization to reduce the required number of gradient directions to resolve crossing FOs, and the residual bootstrap used in previous methods is not applicable to these models. In this work, we propose a probabilistic tractography algorithm named Lasso bootstrap tractography(LBT) for the models that incorporate sparsity. Using a fixed tensor basis and a sparsity assumption, diffusion signals are modeled using a Lasso formulation. With the residuals from the Lasso model, a distribution of diffusion signals is obtained according to a modified Lasso bootstrap strategy. FOs are then estimated from the synthesized diffusion signals by an algorithm that improves FO estimation by enforcing spatial consistency of FOs. Finally, streamlining fiber tracking is performed with the computed FOs. The LBT algorithm was evaluated on simulated and real dMRI data both qualitatively and quantitatively. Results demonstrate that LBT outperforms state-of-the-art algorithms.

Bootstrap Tests of Mean-Variance Efficiency with Multiple Portfolio Groupings

We propose double bootstrap methods to test the mean-variance efficiency hypothesis when multiple portfolio groupings of the test assets are considered jointly rather than individually. A direct test of the joint null hypothesis may not be possible with standard methods when the total number of test assets grows large relative to the number of available time-series observations, since the estimate of the disturbance covariance matrix eventually becomes singular. The suggested residual bootstrap procedures based on combining the individual group p-values avoid this problem while controlling the overall significance level. Simulation and empirical results illustrate the usefulness of the joint mean-variance efficiency tests.

Asymptotic properties of the bootstrap unit root test statistic under possibly infinite variance

ABSTRACTIn this article, the unit root test for the AR(1) model is discussed, under the condition that the innovations of the model are in the domain of attraction of the normal law with possibly infinite variances. By using residual bootstrap with sample size m < n (n being the size of the original sample), we bootstrap the least-squares estimator of the autoregressive parameter. Under some mild assumptions, we prove that the null distribution of the unit root test statistic based on the least-square estimator of the autoregressive parameter can be approximated by using residual bootstrap.

PENERAPAN BOOTSTRAP DALAM METODE MINIMUM COVARIANCE DETERMINANT (MCD) DAN LEAST MEDIAN OF SQUARES (LMS) PADA ANALISIS REGRESI LINIER BERGANDA

Ordinary Least Squares (OLS) Method is a good method to estimate regression parameters when there is no violation in classical assumptions, such as the existence of outlier. Outliers can lead to biased parameters estimator, therefore we need a method that can may not affected by the existence of outlier such as Minimum Covariance Determinant (MCD) and Least Median of Squares (LMS). However, the application of this method is less accurate when it is used for small data. To overcome this problem, it was aplicated bootstrap method in MCD and LMS to determine the comparison of bias in parameters which were produced by both methods in dealing outlier in small data. The used bootstrap method in this study was the residual bootstrap that works by resampling the residuals. By using 95% and 99% confidence level and 5%, 10% and 15% outlier percentage, MCD-bootstrap and LMS-bootstrap give value of parameter estimators which were unbias for all percentage of outlier. We also found that the widht of range which produced by MCD-bootstrap method was shorter than LMS-bootstrap method produced. This indicates that MCD-bootstrap method was a better method than LMS-bootstrap method.

An at-site flood estimation method in the context of nonstationarity II. Statistical analysis of floods in Quebec

Summary This paper, the second of a two-part paper, investigates the nonstationary behaviour of flood peaks in Quebec (Canada) by analyzing the annual maximum flow series (AMS) available for the common 1966–2001 period from a network of 32 watersheds. Temporal trends in the mean of flood peaks were examined by the nonparametric Mann–Kendall test. The significance of the detected trends over the whole province is also assessed by a bootstrap test that preserves the cross-correlation structure of the network. Furthermore, The LM–NS method (introduced in the first part) is used to parametrically model the AMS, investigating its applicability to real data, to account for temporal trends in the moments of the time series. In this study two probability distributions (GEV & Gumbel) were selected to model four different types of time-varying moments of the historical time series considered, comprising eight competing models. The selected models are: two stationary models (GEV0 & Gumbel0), two nonstationary models in the mean as a linear function of time (GEV1 & Gumbel1), two nonstationary models in the mean as a parabolic function of time (GEV2 & Gumbel2), and two nonstationary models in the mean and the log standard deviation as linear functions of time (GEV11 & Gumbel11). The eight models were applied to flood data available for each watershed and their performance was compared to identify the best model for each location. The comparative methodology involves two phases: (1) a descriptive ability based on likelihood-based optimality criteria such as the Bayesian Information Criterion (BIC) and the deviance statistic; and (2) a predictive ability based on the residual bootstrap. According to the Mann–Kendall test and the LM–NS method, a quarter of the analyzed stations show significant trends in the AMS. All of the significant trends are negative, indicating decreasing flood magnitudes in Quebec. It was found that the LM–NS method could provide accurate flood estimates in the context of nonstationarity. The results have indicated the importance of taking into consideration the nonstationary behaviour of the flood series in order to improve the quality of flood estimation. The results also provided a general impression on the possible impacts of climate change on flood estimation in the Quebec province.

Towards Efficiency in the Residual and Parametric Bootstrap Techniques

There are many bootstrap methods that can be used for statistical analysis especially in econometrics, biometrics, Statistics, Sampling and so on. The sole aim of this paper is to ascertain the accuracy and efficiency of the estimates from the independent and identically distributed (iid) simple linear regression (SLR) model under a variety of assessment conditions using bootstrap techniques. Analysis was carried out using S-plus statistical package on hypothetical data sets from a normal distribution with different group proficiency levels to buttress the arguments in the paper. In the course of the analysis, 268,800 scenarios were replicated 1000 times. The result shows a significant difference between the performances of the bootstrap methods used, namely; residual and parametric bootstrap techniques. From the analysis, the largest bias and standard error were always associated with model HP311 while the smallest bias and standard error values were associated with models HR311. The exception was found in the group proficiency level 3- N (1, 0.25), when the sample sizes were 200, 1000 and 10000 instead of model HR311 producing the smallest bias and standard error, model RP311 did. The significantly better performance of the residual bootstrap indicates the possible use of this technique in assessment of comparative performance and the capability of yielding very accurate, consistent, faster and extra-ordinarily reliable statistical inference under several assessment conditions.

CLME: An R Package for Linear Mixed Effects Models under Inequality Constraints.

In many applications researchers are typically interested in testing for inequality constraints in the context of linear fixed effects and mixed effects models. Although there exists a large body of literature for performing statistical inference under inequality constraints, user friendly statistical software for implementing such methods is lacking, especially in the context of linear fixed and mixed effects models. In this article we introduce CLME, a package in the R language that can be used for testing a broad collection of inequality constraints. It uses residual bootstrap based methodology which is reasonably robust to non-normality as well as heteroscedasticity. The package is illustrated using two data sets. The package also contains a graphical interface built using the shiny package.

Identifying preoperative language tracts and predicting postoperative functional recovery using HARDI q-ball fiber tractography in patients with gliomas.

OBJECT Diffusion MRI has uniquely enabled in vivo delineation of white matter tracts, which has been applied to the segmentation of eloquent pathways for intraoperative mapping. The last decade has also seen the development from earlier diffusion tensor models to higher-order models, which take advantage of high angular resolution diffusion-weighted imaging (HARDI) techniques. However, these advanced methods have not been widely implemented for routine preoperative and intraoperative mapping. The authors report on the application of residual bootstrap q-ball fiber tracking for routine mapping of potentially functional language pathways, the development of a system for rating tract injury to evaluate the impact on clinically assessed language function, and initial results predicting long-term language deficits following glioma resection. METHODS The authors have developed methods for the segmentation of 8 putative language pathways including dorsal phonological pathways and ventral semantic streams using residual bootstrap q-ball fiber tracking. Furthermore, they have implemented clinically feasible preoperative acquisition and processing of HARDI data to delineate these pathways for neurosurgical application. They have also developed a rating scale based on the altered fiber tract density to estimate the degree of pathway injury, applying these ratings to a subset of 35 patients with pre- and postoperative fiber tracking. The relationships between specific pathways and clinical language deficits were assessed to determine which pathways are predictive of long-term language deficits following surgery. RESULTS This tracking methodology has been routinely implemented for preoperative mapping in patients with brain gliomas who have undergone awake brain tumor resection at the University of California, San Francisco (more than 300 patients to date). In this particular study the authors investigated the white matter structure status and language correlation in a subcohort of 35 subjects both pre- and postsurgery. The rating scales developed for fiber pathway damage were found to be highly reproducible and provided significant correlations with language performance. Preservation of the left arcuate fasciculus (AF) and the temporoparietal component of the superior longitudinal fasciculus (SLF-tp) was consistent in all patients without language deficits (p < 0.001) at the long-term follow-up. Furthermore, in patients with short-term language deficits, the AF and/or SLF-tp were affected, and damage to these 2 pathways was predictive of a long-term language deficit (p = 0.005). CONCLUSIONS The authors demonstrated the successful application of q-ball tracking in presurgical planning for language pathways in brain tumor patients and in assessing white matter tract integrity postoperatively to predict long-term language dysfunction. These initial results predicting long-term language deficits following tumor resection indicate that postoperative injury to dorsal language pathways may be prognostic for long-term clinical language deficits. Study results suggest the importance of dorsal stream tract preservation to reduce language deficits in patients undergoing glioma resection, as well as the potential prognostic value of assessing postoperative injury to dorsal language pathways to predict long-term clinical language deficits.

Approximating and reducing bias in 2SLS estimation of dynamic simultaneous equation models

An order O(1/T) approximation is made to the bias in 2SLS estimation of a dynamic simultaneous equation model, building on similar large-T moment approximations for non-dynamic models. The expression is long because it contains two distinct parts: a part due to the simultaneity which is directly related to the Nagar bias and a part due to the dynamics which has many component terms. However, the analytically corrected 2SLS estimators resulting from this approximation perform well in terms of remaining estimation bias. The biases of these estimators are compared with the Quenouille half-sample jackknife and the residual bootstrap for 2SLS in dynamic models, and are found to be competitive. The Monte Carlo and bias approximation also suggest that the bias in estimating endogenous variable coefficients in dynamic simultaneous equation models is non monotonic in the sample size, contrary to the well known theoretical result for static models. The effect of using weaker instruments on our numerical and Monte Carlo results is explored.

Assessing uncertainties in surface water security: An empirical multimodel approach

AbstractVarious uncertainties are involved in the representation of processes that characterize interactions among societal needs, ecosystem functioning, and hydrological conditions. Here we develop an empirical uncertainty assessment of water security indicators that characterize scarcity and vulnerability, based on a multimodel and resampling framework. We consider several uncertainty sources including those related to (i) observed streamflow data; (ii) hydrological model structure; (iii) residual analysis; (iv) the method for defining Environmental Flow Requirement; (v) the definition of critical conditions for water provision; and (vi) the critical demand imposed by human activities. We estimate the overall hydrological model uncertainty by means of a residual bootstrap resampling approach, and by uncertainty propagation through different methodological arrangements applied to a 291 km2 agricultural basin within the Cantareira water supply system in Brazil. Together, the two‐component hydrograph residual analysis and the block bootstrap resampling approach result in a more accurate and precise estimate of the uncertainty (95% confidence intervals) in the simulated time series. We then compare the uncertainty estimates associated with water security indicators using a multimodel framework and the uncertainty estimates provided by each model uncertainty estimation approach. The range of values obtained for the water security indicators suggests that the models/methods are robust and performs well in a range of plausible situations. The method is general and can be easily extended, thereby forming the basis for meaningful support to end‐users facing water resource challenges by enabling them to incorporate a viable uncertainty analysis into a robust decision‐making process.

Goodness of fit in nonlinear dynamics: Misspecified rates or misspecified states?

This paper introduces diagnostic tests for the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation, misspecification of functional forms in rate equations, and omission of dynamic variables in the description of the system. We represent lack of fit by allowing a parameter vector to vary over time, and propose generic testing procedures that do not rely on specific alternative models. Instead, different sources for lack of fit are characterized in terms of nonparametric relationships among latent variables. The tests are carried out through a combination of residual bootstrap and permutation methods. We demonstrate the effectiveness of these tests on simulated data and on real data from laboratory ecological experiments and electro-cardiogram data.

Statistical uncertainty of eddy covariance CO2 fluxes inferred using a residual bootstrap approach

High-frequency eddy-covariance measurements of net ecosystem CO2 exchange (NEE) with the atmosphere are valuable resources for model parameterization, calibration, and validation. However, uncertainties in measured data, i.e., data gaps and inherent random errors, create problems for researchers attempting to quantify uncertainties in model projections of terrestrial ecosystem carbon cycling. Here, we demonstrate that a model-data fusion method (residual bootstrap) produces defensible annual NEE sums, through mimicking the behavior of random errors, filling missing values, and simulating gap-filling biases. This study estimated annual NEE sums for 53 site-years based on nine eddy-covariance tower sites in the USA, and found that our annual estimates were, in most cases, comparable in magnitude with those obtained from AmeriFlux gap-filled data. Additionally, compared to the AmeriFlux standardized gap-filling, our approach provides better NEE estimates for moderate to longer, and more frequent, data gaps. Annual accumulated uncertainties in NEE at the 95% confidence level were ±30gCm−2year−1 for evergreen needleleaf forests; ±60gCm−2year−1 for deciduous broadleaf forests; and ±80gCm−2year−1 for croplands. The residual bootstrap performed worst when gap length was greater than one month or data exclusion greater than 90% during the growing season, common to other gap-filling techniques. However, this study produced robust results for most site years when monthly data coverage during the growing season is not extremely low. We therefore suggest that the inclusion of NEE uncertainty estimates and better estimation for moderate to longer, and more frequent, data gaps as provided by the residual bootstrap approach can be beneficial for ecosystem model evaluation.

Econometric Model of the Czech Life Insurance Market

The aim of the article is to introduce a complex econometric model of cash-lows for the Czech life insurance market. Namely, technical-actuarial links among insurance variables observed in annually published summary balance sheets of life insurers are described by means of an econometric system of linear simultaneous equations. The suggested model is statistically veri ed and thus it can provide useful economic interpretations. Further, adjusted residual bootstrapping is introduced in this context as a straightforward alternative which can solve possible problems with questionable asymptotic distribution properties of residuals. This technique can be applied e.g. for signi cance testing purposes. Finally, an important practical illustration of scenario analysis is considered. Such an analysis might be really useful, e.g. for internal calculations of the Czech life insurers, nancial planning or stress testing in the framework of Solvency II. Two general approaches are presented: deterministic and stochastic. The second one is capable of delivering various empirical probabilities concerning possible future developments.

PENERAPAN METODE BOOTSTRAP RESIDUAL DALAM MENGATASI BIAS PADA PENDUGA PARAMETER ANALISIS REGRESI

Statistical analysis which aims to analyze a linear relationship between the independent variable and the dependent variable is known as regression analysis. To estimate parameters in a regression analysis method commonly used is the Ordinary Least Square (OLS). But the assumption is often violated in the OLS, the assumption of normality due to one outlier. As a result of the presence of outliers is parameter estimators produced by the OLS will be biased. Bootstrap Residual is a bootstrap method that is applied to the residual resampling process. The results showed that the residual bootstrap method is only able to overcome the bias on the number of outliers 5% with 99% confidence intervals. The resulting parameters estimators approach the residual bootstrap values ??OLS initial allegations were also able to show that the bootstrap is an accurate prediction tool.

Beyond crossing fibers: bootstrap probabilistic tractography using complex subvoxel fiber geometries.

Diffusion magnetic resonance imaging fiber tractography is a powerful tool for investigating human white matter connectivity in vivo. However, it is prone to false positive and false negative results, making interpretation of the tractography result difficult. Optimal tractography must begin with an accurate description of the subvoxel white matter fiber structure, includes quantification of the uncertainty in the fiber directions obtained, and quantifies the confidence in each reconstructed fiber tract. This paper presents a novel and comprehensive pipeline for fiber tractography that meets the above requirements. The subvoxel fiber geometry is described in detail using a technique that allows not only for straight crossing fibers but for fibers that curve and splay. This technique is repeatedly performed within a residual bootstrap statistical process in order to efficiently quantify the uncertainty in the subvoxel geometries obtained. A robust connectivity index is defined to quantify the confidence in the reconstructed connections. The tractography pipeline is demonstrated in the human brain.

Robustness of Bootstrap in Instrumental Variable Regression

This paper studies robustness of bootstrap inference methods for instrumental variable (IV) regression models. We consider test statistics for parameter hypotheses based on the IV estimator and generalized method of trimmed moments (GMTM) estimator introduced by Čížek (2008, 2009), and compare the pairs and implied probability bootstrap approximations for these statistics by applying the finite sample breakdown point theory. In particular, we study limiting behaviors of the bootstrap quantiles when the values of outliers diverge to infinity but the sample size is held fixed. The outliers are defined as anomalous observations that can arbitrarily change the value of the statistic of interest. We analyze both just- and overidentified cases and discuss implications of the breakdown point analysis to the size and power properties of bootstrap tests. We conclude that the implied probability bootstrap test using the statistic based on the GMTM estimator shows desirable robustness properties. Simulation studies endorse this conclusion. An empirical example based on Romer's (1993) study on the effect of openness of countries to inflation rates is presented. Several extensions including the analysis for the residual bootstrap are provided.

On generalized degrees of freedom with application in linear mixed models selection

The concept of degrees of freedom plays an important role in statistical modeling and is commonly used for measuring model complexity. The number of unknown parameters, which is typically used as the degrees of freedom in linear regression models, may fail to work in some modeling procedures, in particular for linear mixed effects models. In this article, we propose a new definition of generalized degrees of freedom in linear mixed effects models. It is derived from using the sum of the sensitivity of the expected fitted values with respect to their underlying true means. We explore and compare data perturbation and the residual bootstrap to empirically estimate model complexity. We also show that this empirical generalized degrees of freedom measure satisfies some desirable properties and is useful for the selection of linear mixed effects models.

Frontal white matter tracts sustaining speech production in primary progressive aphasia.

In primary progressive aphasia (PPA), speech and language difficulties are caused by neurodegeneration of specific brain networks. In the nonfluent/agrammatic variant (nfvPPA), motor speech and grammatical deficits are associated with atrophy in a left fronto-insular-striatal network previously implicated in speech production. In vivo dissection of the crossing white matter (WM) tracts within this "speech production network" is complex and has rarely been performed in health or in PPA. We hypothesized that damage to these tracts would be specific to nfvPPA and would correlate with differential aspects of the patients' fluency abilities. We prospectively studied 25 PPA and 21 healthy individuals who underwent extensive cognitive testing and 3 T MRI. Using residual bootstrap Q-ball probabilistic tractography on high angular resolution diffusion-weighted imaging (HARDI), we reconstructed pathways connecting posterior inferior frontal, inferior premotor, insula, supplementary motor area (SMA) complex, striatum, and standard ventral and dorsal language pathways. We extracted tract-specific diffusion tensor imaging (DTI) metrics to assess changes across PPA variants and perform brain-behavioral correlations. Significant WM changes in the left intrafrontal and frontostriatal pathways were found in nfvPPA, but not in the semantic or logopenic variants. Correlations between tract-specific DTI metrics with cognitive scores confirmed the specific involvement of this anterior-dorsal network in fluency and suggested a preferential role of a posterior premotor-SMA pathway in motor speech. This study shows that left WM pathways connecting the speech production network are selectively damaged in nfvPPA and suggests that different tracts within this system are involved in subcomponents of fluency. These findings emphasize the emerging role of diffusion imaging in the differential diagnosis of neurodegenerative diseases.

Uncertainty estimation in diffusion MRI using the nonlocal bootstrap.

In this paper, we propose a new bootstrap scheme, called the nonlocal bootstrap (NLB) for uncertainty estimation. In contrast to the residual bootstrap, which relies on a data model, or the repetition bootstrap, which requires repeated signal measurements, NLB is not restricted by the data structure imposed by a data model and obviates the need for time-consuming multiple acquisitions. NLB hinges on the observation that local imaging information recurs in an image. This self-similarity implies that imaging information coming from spatially distant (nonlocal) regions can be exploited for more effective estimation of statistics of interest. Evaluations using in silico data indicate that NLB produces distribution estimates that are in closer agreement with those generated using Monte Carlo simulations, compared with the conventional residual bootstrap. Evaluations using in vivo data demonstrate that NLB produces results that are in agreement with our knowledge on white matter architecture.