The Bootstrap-Method: Discussion and Proposal for Improvement / Das bootstrap-Verfahren: Diskussion und Verbesserungsvorschlag

1998 ◽  
Vol 217 (1) ◽  
Author(s):  
Hans Schneeberger
Keyword(s):  
Bootstrap Method ◽  
Law School ◽  
Mean Deviation ◽  
Alternative Method ◽  
Doubling Method ◽  
The Mean ◽  
The Bootstrap Method

SummaryWith Efron’s law-school example the bootstrap method is compared with an alternative method, called doubling. It is shown, that the mean deviation of the estimator is always smaller for the doubling method.

scholarly journals Uncertainty of the Electricity Emission Factor Incorporating the Uncertainty of the Fuel Emission Factors

Energies ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5697
Author(s):  
Kun Mo LEE ◽  
Min Hyeok LEE
Keyword(s):  
Power Generation ◽  
Emission Factor ◽  
Bootstrap Method ◽  
Ghg Emissions ◽  
Original Data ◽  
Emission Factors ◽  
Ghg Emission ◽  
Data Set ◽  
The Mean ◽  
The Bootstrap Method

Greenhouse gas (GHG) emission from electricity generation has been recognized as one of the most significant contributors to global warming. The GHG emission factor of electricity (hereafter, electricity emission factor) can be expressed as a function of three different (average, minimum, and maximum) fuel emission factors, monthly fuel consumption, and monthly net power generation. Choosing the average fuel emission factor over the minimum and maximum fuel emission factors is the cause of uncertainty in the electricity emission factor, and thus GHG emissions of the power generation. The uncertainties of GHG emissions are higher than those of the electricity emission factor, indicating that the uncertainty of GHG emission propagates in the GHG emission computation model. The bootstrapped data were generated by applying the bootstrap method to the original data set which consists of a 60-monthly average, and minimum and maximum electricity emission factors. The bootstrapped data were used for computing the mean, confidence interval (CI), and percentage uncertainty (U) of the electricity emission factor. The CI, mean, and U were [0.431, 0.443] kg CO2-eq/kWh, 0.437 kg CO2-eq/kwh, and 2.56%, respectively.

scholarly journals Estimation of Uncertainty in Airborne LiDAR Inventories Using Approaches Based on Bootstrapping-Pairs Methods

Forests ◽  
2020 ◽  
Vol 11 (12) ◽  
pp. 1305
Author(s):  
Simón Sandoval ◽  
Ramón Bustamante-Ortega
Keyword(s):  
Bootstrap Method ◽  
Airborne Lidar ◽  
Population Estimates ◽  
Residual Variance ◽  
Average Volume ◽  
Pair Method ◽  
The Mean ◽  
Variance Estimates ◽  
The Relationship ◽  
The Bootstrap Method

LiDAR inventories were carried out to estimate the mean volume and variance in Eucalyptus globulus and Eucalyptus nitens stands. Uncertainty of the population estimates was examined using approximations based on the bootstrap method. Three methods were tested, the traditional bootstrapping-pair method (Method 1) and two additional methods in which the residual variance of the models was incorporated. Method 2 incorporated the residual variance in homoscedastic structure and Method 3 incorporated the heteroscedastic residual variance. Bootstrapping-pairs based on Method 3 generated similar estimates for the mean volume and slightly higher estimates for the variance as the traditional method (Method 1). Variance estimates obtained with the traditional bootstrapping-pairs method could be biased due to the presence of heteroscedasticity. Method 3 was found to best estimate the variance of the mean volume in LiDAR inventories, when the models that describe the relationship between stand variables and LiDAR metrics do not meet the assumption of homoscedasticity. It is shown that the uncertainty of the estimation of the average volume decreased in stands with a larger area, stabilizing the uncertainty of estimates in stands with areas larger than 50 hectares. Our results suggest that the residual variance in the heteroscedastic structure must be incorporated to avoid bias when bootstrapping-pairs are used in small area stands (less than 5 hectares).

DFT Benchmark Study of the O--O Bond Dissociation Energy in Peroxides Validated with High-Level Ab-Initio Calculations

2019 ◽  
Author(s):  
Danilo Carmona ◽  
Pablo Jaque ◽  
Esteban Vöhringer-Martinez
Keyword(s):  
Reference Value ◽  
Basis Set ◽  
Basis Sets ◽  
Mean Deviation ◽  
Bond Dissociation ◽  
Dissociation Energies ◽  
The Mean ◽  
Experimental Values ◽  
High Level ◽  
Almost All

<div><div><div><p>Peroxides play a central role in many chemical and biological pro- cesses such as the Fenton reaction. The relevance of these compounds lies in the low stability of the O–O bond which upon dissociation results in radical species able to initiate various chemical or biological processes. In this work, a set of 64 DFT functional-basis set combinations has been validated in terms of their capability to describe bond dissociation energies (BDE) for the O–O bond in a database of 14 ROOH peroxides for which experimental values ofBDE are available. Moreover, the electronic contributions to the BDE were obtained for four of the peroxides and the anion H2O2− at the CBS limit at CCSD(T) level with Dunning’s basis sets up to triple–ζ quality provid- ing a reference value for the hydrogen peroxide anion as a model. Almost all the functionals considered here yielded mean absolute deviations around 5.0 kcal mol−1. The smallest values were observed for the ωB97 family and the Minnesota M11 functional with a marked basis set dependence. Despite the mean deviation, order relations among BDE experimental values of peroxides were also considered. The ωB97 family was able to reproduce the relations correctly whereas other functionals presented a marked dependence on the chemical nature of the R group. Interestingly, M11 functional did not show a very good agreement with the established order despite its good performance in the mean error. The obtained results support the use of similar validation strategies for proper prediction of BDE or other molecular properties by DF Tmethods in subsequent related studies.</p></div></div></div>

Der Sommer und Herbst 2003 aus phänologischer Sicht | Summer and autumn 2003 from a phenological point of view

2004 ◽  
Vol 155 (5) ◽  
pp. 142-145 ◽  
Author(s):  
Claudio Defila
Keyword(s):  
Time Series ◽  
New Record ◽  
Point Of View ◽  
Late Spring ◽  
Mean Deviation ◽  
Leaf Shedding ◽  
The Mean ◽  
Very High ◽  
Selection Of

The record-breaking heatwave of 2003 also had an impact on the vegetation in Switzerland. To examine its influences seven phenological late spring and summer phases were evaluated together with six phases in the autumn from a selection of stations. 30% of the 122 chosen phenological time series in late spring and summer phases set a new record (earliest arrival). The proportion of very early arrivals is very high and the mean deviation from the norm is between 10 and 20 days. The situation was less extreme in autumn, where 20% of the 103 time series chosen set a new record. The majority of the phenological arrivals were found in the class «normal» but the class«very early» is still well represented. The mean precocity lies between five and twenty days. As far as the leaf shedding of the beech is concerned, there was even a slight delay of around six days. The evaluation serves to show that the heatwave of 2003 strongly influenced the phenological events of summer and spring.

scholarly journals Correlation between fundus autofluorescence and visual function in patients with cone-rod dystrophy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Satoru Kanda ◽  
Takumi Hara ◽  
Ryosuke Fujino ◽  
Keiko Azuma ◽  
Hirotsugu Soga ◽  
...  
Keyword(s):  
Visual Field ◽  
Significant Relationship ◽  
Fundus Autofluorescence ◽  
Univariate Analysis ◽  
Retrospective Chart Review ◽  
Mean Deviation ◽  
Wide Field ◽  
The Mean ◽  
The Relationship ◽  
Field Imaging

AbstractThis study aimed to investigate the relationship between autofluorescence (AF) signal measured with ultra-wide field imaging and visual functions in patients with cone-rod dystrophy (CORD). A retrospective chart review was performed for CORD patients. We performed the visual field test and fundus autofluorescence (FAF) measurement and visualized retinal structures with optical coherence tomography (OCT) on the same day. Using binarised FAF images, we identified a low FAF area ratio (LFAR: low FAF/30°). Relationships between age and logMAR visual acuity (VA), central retinal thickness (CRT), central choroidal thickness (CCT), mean deviation (MD) value, and LFAR were investigated. Thirty-seven eyes of 21 CORD patients (8 men and 13 women) were enrolled. The mean patient age was 49.8 years. LogMAR VA and MD were 0.52 ± 0.47 and − 17.91 ± 10.59 dB, respectively. There was a significant relationship between logMAR VA and MD (p = 0.001). LogMAR VA significantly correlated with CRT (p = 0.006) but not with other parameters. Conversely, univariate analysis suggested a significant relationship between MD and LFAR (p = 0.001). In the multivariate analysis, LFAR was significantly associated with MD (p = 0.002). In conclusion, it is useful to measure the low FAF area in patients with CORD. The AF measurement reflects the visual field deterioration but not VA in CORD.

scholarly journals Statistical Estimates of the Pulsar Glitch Activity

Universe ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 8
Author(s):  
Alessandro Montoli ◽  
Marco Antonelli ◽  
Brynmor Haskell ◽  
Pierre Pizzochero
Keyword(s):  
Linear Regression ◽  
Upper Bound ◽  
Bootstrap Method ◽  
Waiting Times ◽  
Statistical Estimates ◽  
Equal Variance ◽  
Linear Fit ◽  
The Moment ◽  
The Bootstrap Method

A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust.

Relationship between mean follow-up intraocular pressure, rates of visual field progression and current target intraocular pressure guidelines

2020 ◽  
pp. bjophthalmol-2020-317406
Author(s):  
Bruna Melchior ◽  
Carlos Gustavo De Moraes ◽  
Jayter S Paula ◽  
George A Cioffi ◽  
Christopher A Girkin ◽  
...  
Keyword(s):  
Intraocular Pressure ◽  
Visual Field ◽  
Treatment Guidelines ◽  
Evaluation Study ◽  
Mean Deviation ◽  
Racial Groups ◽  
Current Guideline ◽  
Registration Number ◽  
The Mean

AimsTo investigate if eyes presenting intraocular pressure (IOP) within the limits of current guideline-driven target IOP indeed experience slow rates of glaucomatous visual field (VF) progression.MethodsA total of 8598 24-2 VF tests from 603 eyes from the African Descent and Glaucoma Evaluation Study with manifest glaucoma were included. The sample was split into three groups based on baseline VF mean deviation (MD): G1 (better than −5.0 dB), G2 (−5.0 to −10 dB) and G3 (worse than −10 dB). We investigated the relationship between existing target IOP guidelines and rates of MD progression in these groups.ResultsFor stable eyes, the medians and IQR of the mean follow-up IOP were G1=15.0 mmHg (IQR: 13.1 to 17.7), G2=13.2 mmHg (IQR: 11.6 to 14.3) and G3=11.9 mmHg (IQR: 10.1 to 13.8) (p<0.01). When considering the mean follow-up IOP within the limits proposed by current guidelines, the median MD slopes were: −0.20 dB/y (IQR: −0.43 to −0.02) for G1<21 mmHg, −0.19 dB/y (IQR: −0.51 to −0.01) for G2<18 mmHg and −0.15 dB/y (IQR: −0.47 to 0.05) for G3<15 mmHg (p=0.63). There were no significant differences between racial groups.ConclusionIn a sample of patients with manifest glaucoma, despite substantial variability between eyes, adherence to treatment guidelines helped slow the rates of global VF progression at various stages of disease.Trial registration numberclinicaltrials.gov Identifier: NCT00221923.

Moments of the mean deviation

Biometrika ◽  
1954 ◽  
Vol 41 (3-4) ◽  
pp. 541-542
Author(s):  
A. R. KAMAT
Keyword(s):  
Mean Deviation ◽  
The Mean
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