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Bootstrap Confidence Intervals (bootstrap + confidence_interval)
Selected AbstractsThreshold changes in vegetation along a grazing gradient in Mongolian rangelandsJOURNAL OF ECOLOGY, Issue 1 2008Takehiro Sasaki Summary 1The concept of threshold has become important in ecology, but the nature of potential threshold responses of vegetation to grazing in rangeland ecosystems remains poorly understood. We aimed to identify ecological thresholds in vegetation changes along a grazing gradient and to examine whether threshold changes were expressed similarly at a variety of ecological sites. 2To accomplish this, we surveyed the vegetation along grazing gradients at 10 ecological sites, each located at different landscape positions in Mongolia's central and southern rangelands. Evidence for a threshold in changes in floristic composition along the grazing gradient was examined by comparing linear models of the data with nonlinear models fitted using an exponential curve, an inverse curve, a piecewise regression and a sigmoid logistic curve. 3Three nonlinear models (piecewise, exponential and sigmoid) provided a much better fit to the data than the linear models, highlighting the presence of a discontinuity in vegetation changes along the grazing gradient. The shapes of the best-fit models and their fit to the data were generally similar across sites, indicating that the changes in floristic composition were relatively constant below a threshold level of grazing, after which the curve changed sharply. 4Except for two sites, the best-fit models had relatively narrow bootstrap confidence intervals (95% CI), especially around threshold points or zones where the rate of change accelerated, emphasizing that our results were robust and conclusive. 5Synthesis. Our study provided strong evidence for the existence of ecological thresholds in vegetation change along a grazing gradient across all ecological sites. This suggests that vegetation responses to grazing in the study areas are essentially nonlinear. The recognition that real threshold changes exist in real grazing gradients will help land managers to prevent the occurrence of undesirable states and promote the occurrence of desirable states, and will therefore permit a major step forward in the sustainable management of rangeland ecosystems. [source] Application of the parametric bootstrap method to determine statistical errors in quantitative X-ray microanalysis of thin filmsJOURNAL OF MICROSCOPY, Issue 1 2007ALDO ARMIGLIATO Summary We applied the parametric bootstrap to the X-ray microanalysis of Si-Ge binary alloys, in order to assess the dependence of the Ge concentrations and the local film thickness, obtained by using previously described Monte Carlo methods, on the precision of the measured intensities. We show how it is possible by this method to determine the statistical errors associated with the quantitative analysis performed in sample regions of different composition and thickness, but by conducting only one measurement. We recommend the use of the bootstrap for a broad range of applications for quantitative microanalysis to estimate the precision of the final results and to compare the performances of different methods to each other. Finally, we exploited a test based on bootstrap confidence intervals to ascertain if, for given X-ray intensities, different values of the estimated composition in two points of the sample are indicative of an actual lack of homogeneity. [source] Midterm cost-effectiveness of the liver transplantation program of England and Wales for three disease groupsLIVER TRANSPLANTATION, Issue 12 2003Louise Longworth Liver transplantation has never been the subject of a randomized controlled trial, and there remains uncertainty about the magnitude of benefit and cost-effectiveness for specific patient groups. This article reports the results of an economic evaluation of adult liver transplantation in England and Wales. Patients placed on the waiting list for a liver transplant were observed over 27 months. The costs and health benefits of a comparison group, representing experience in the absence of liver transplantation, were estimated using a combination of observed data from patients waiting for a transplant and published prognostic models. The analysis focuses on three disease groups, for each of which prognostic models were available: primary biliary cirrhosis (PBC), alcoholic liver disease (ALD), and primary sclerosing cholangitis (PSC). A higher proportion of patients with ALD were assessed for a transplant but not placed on the waiting list. The estimated gain in quality-adjusted life-years from transplantation was positive for each of the disease groups. The mean incremental cost per quality-adjusted life-year (95% bootstrap confidence intervals) from time of listing to 27 months for patients with PBC, ALD, and PSC are £29,000 (£1,000 to £59,000), £48,000 (£12,000 to £83,000) and £21,000 (,£23,000 to £60,000), respectively. In conclusion, liver transplantation increases the survival and health-related quality of life of patients with each of three end-stage liver diseases. However, the extent of this increase differs between different disease groups. Cost-effectiveness estimates were poorer for patients with ALD over the 27-month period than for patients with PBC or PSC. This in part reflects the costs of the higher number of ALD patients assessed for each transplant. [source] On the bootstrap in cube root asymptoticsTHE CANADIAN JOURNAL OF STATISTICS, Issue 1 2006Christian Léger Abstract The authors study the application of the bootstrap to a class of estimators which converge at a nonstandard rate to a nonstandard distribution. They provide a theoretical framework to study its asymptotic behaviour. A simulation study shows that in the case of an estimator such as Chernoff's estimator of the mode, usually the basic bootstrap confidence intervals drastically undercover while the percentile bootstrap intervals overcover. This is a rare instance where basic and percentile confidence intervals, which have exactly the same length, behave in a very different way. In the case of Chernoff's estimator, if the distribution is symmetric, it is possible to bootstrap from a smooth symmetric estimator of the distribution for which the basic bootstrap confidence intervals will have the claimed coverage probability while the percentile bootstrap interval will have an asymptotic coverage of 1! A propos du bootstrap pour des estimateurs convergeant a la vitesse racine cubique Les auteurs étudient l'application du bootstrap à une classe d'estimateurs qui convergent à une vitesse et vers une loi non standard. Ils présentent un cadre théorique pour l'étude de son comportement asymptotique. Une simulation démontre que dans le cas d'un estimateur du mode de Chernoff, la probabilité de couverture de l'intervalle de confiance bootstrap de base est grandement inférieure au niveau prescrit, alors que celle des intervalles de type percentile dépasse le niveau prescrit. C'est un rare cas où les intervalles de confiance de base et percentile ont un comportement si différent malgré des longueurs identiques. Dans le cas de l'estimateur de Chernoff, si la distribution est symétrique, il est possible d'appliquer le bootstrap à partir d'un estimateur lisse et symétrique de la distribution qui mènera à des intervalles bootstrap de base dont la probabilité de couverture asymptotique sera la bonne, alors que celle de l'intervalle percentile convergera vers 1! [source] THE PURCHASING POWER PARITY PERSISTENCE PUZZLE: EVIDENCE FROM BLACK MARKET REAL EXCHANGE RATES,THE MANCHESTER SCHOOL, Issue 4 2008MARIO CERRATO In this paper we analyse the purchasing power parity (PPP) persistence puzzle using a unique data set of black market real exchange rates for 36 emerging market economies and (exact and approximate) median unbiased univariate and panel estimation methods. We construct bootstrap confidence intervals for the half-lives, as well as exact quantiles of the median function for different significance levels using Monte Carlo simulation. Even after accounting for a number of econometric issues, the PPP persistence puzzle is still a striking characteristic of the majority of emerging market countries. However, in a minority of exchange rates, the PPP puzzle is removed. [source] Area under the Free-Response ROC Curve (FROC) and a Related Summary IndexBIOMETRICS, Issue 1 2009Andriy I. Bandos Summary Free-response assessment of diagnostic systems continues to gain acceptance in areas related to the detection, localization, and classification of one or more "abnormalities" within a subject. A free-response receiver operating characteristic (FROC) curve is a tool for characterizing the performance of a free-response system at all decision thresholds simultaneously. Although the importance of a single index summarizing the entire curve over all decision thresholds is well recognized in ROC analysis (e.g., area under the ROC curve), currently there is no widely accepted summary of a system being evaluated under the FROC paradigm. In this article, we propose a new index of the free-response performance at all decision thresholds simultaneously, and develop a nonparametric method for its analysis. Algebraically, the proposed summary index is the area under the empirical FROC curve penalized for the number of erroneous marks, rewarded for the fraction of detected abnormalities, and adjusted for the effect of the target size (or "acceptance radius"). Geometrically, the proposed index can be interpreted as a measure of average performance superiority over an artificial "guessing" free-response process and it represents an analogy to the area between the ROC curve and the "guessing" or diagonal line. We derive the ideal bootstrap estimator of the variance, which can be used for a resampling-free construction of asymptotic bootstrap confidence intervals and for sample size estimation using standard expressions. The proposed procedure is free from any parametric assumptions and does not require an assumption of independence of observations within a subject. We provide an example with a dataset sampled from a diagnostic imaging study and conduct simulations that demonstrate the appropriateness of the developed procedure for the considered sample sizes and ranges of parameters. [source] Estimating the Species Accumulation Curve Using MixturesBIOMETRICS, Issue 2 2005Chang Xuan Mao Summary As a significant tool in ecological studies, the species accumulation curve or the collector's curve is the graph of the expected number of detected species as a function of sampling effort. The problem of estimating the species accumulation curve based on an empirical data set arising from quadrat sampling is studied in a nonparametric binomial mixture model. It will be shown that estimating the species accumulation curve not only is independent of the unknown number of species but also includes estimating the number of species as a limiting case. For the purpose of interpolation, moment-based estimators, associated with asymptotic confidence intervals, are developed from several points of view. A likelihood-based procedure is developed for the purpose of extrapolation, associated with bootstrap confidence intervals. The proposed methods are illustrated by ecological data sets. [source] | |||||||||||||