scholarly journals The Smoothed Bootstrap Fine-Tuning

2019 ◽  
Vol 1 (1) ◽  
pp. 716-723
Author(s):  
Renata Dwornicka ◽  
Andrii Goroshko ◽  
Jacek Pietraszek
Keyword(s):  
Probability Distribution ◽  
Empirical Distribution ◽  
Bootstrap Method ◽  
Small Sample ◽  
Fine Tuning ◽  
Smoothed Bootstrap ◽  
Full Probability ◽  
The Bootstrap Method

AbstractThe bootstrap method is a well-known method to gather a full probability distribution from the dataset of a small sample. The simple bootstrap i.e. resampling from the raw dataset often leads to a significant irregularities in a shape of resulting empirical distribution due to the discontinuity of a support. The remedy for these irregularities is the smoothed bootstrap: a small random shift of source points before each resampling. This shift is controlled by specifically selected distributions. The key issue is such parameter settings of these distributions to achieve the desired characteristics of the empirical distribution. This paper describes an example of this procedure.

scholarly journals Reliability Evaluation for the Running State of the Manufacturing System Based on Poor Information

2016 ◽  
Vol 2016 ◽  
pp. 1-19 ◽  
Author(s):  
Xintao Xia ◽  
Wenhuan Zhu ◽  
Bin Liu
Keyword(s):  
Probability Distribution ◽  
Product Quality ◽  
Manufacturing System ◽  
Evaluation Method ◽  
Probability Distributions ◽  
Bootstrap Method ◽  
Maximum Entropy Principle ◽  
Reliability Evaluation ◽  
Small Sample ◽  
Inspection Data

The output performance of the manufacturing system has a direct impact on the mechanical product quality. For guaranteeing product quality and production cost, many firms try to research the crucial issues on reliability of the manufacturing system with small sample data, to evaluate whether the manufacturing system is capable or not. The existing reliability methods depend on a known probability distribution or vast test data. However, the population performances of complex systems become uncertain as processing time; namely, their probability distributions are unknown, if the existing methods are still taken into account; it is ineffective. This paper proposes a novel evaluation method based on poor information to settle the problems of reliability of the running state of a manufacturing system under the condition of small sample sizes with a known or unknown probability distribution. Via grey bootstrap method, maximum entropy principle, and Poisson process, the experimental investigation on reliability evaluation for the running state of the manufacturing system shows that, under the best confidence levelP=0.95, if the reliability degree of achieving running quality isr>0.65, the intersection area between the inspection data and the intrinsic data isA(T)>0.3and the variation probability of the inspection data isPB(T)≤0.7, and the running state of the manufacturing system is reliable; otherwise, it is not reliable. And the sensitivity analysis regarding the size of the samples can show that the size of the samples has no effect on the evaluation results obtained by the evaluation method. The evaluation method proposed provides the scientific decision and suggestion for judging the running state of the manufacturing system reasonably, which is efficient, profitable, and organized.

Parameter distribution characteristics of material fatigue life using improved bootstrap method

2018 ◽  
Vol 28 (5) ◽  
pp. 772-793 ◽  
Author(s):  
Minghui Zhang ◽  
Xintian Liu ◽  
Yansong Wang ◽  
Xiaolan Wang
Keyword(s):  
Fatigue Life ◽  
Test Data ◽  
Bootstrap Method ◽  
Small Sample ◽  
Statistical Characteristics ◽  
Average Error ◽  
Parameter Distribution ◽  
Virtual Test ◽  
Sample Data ◽  
The Bootstrap Method

The bootstrap method is mostly used to estimate statistical characteristics of small sample data. However, the limitations of the bootstrap method itself lead to a reduction in the reliability of small-sample estimates. In this article, an improved bootstrap method is developed to address this problem. In the statistically significant error range (the sample average error and the limit error of sampling) of the original single sample data, expanding the virtual test data that obey two distributions to overcome the limitations of the bootstrap method itself. This article compares and analyses these two methods through the case; the result indicates that the improved bootstrap method can enhance the reliability of the estimation results without changing its probability distribution. We also discussed how to reduce the fluctuation of the improved bootstrap method. And the effectiveness and feasibility of this improved method are discussed in the analysis of fatigue life test data.

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.

scholarly journals Reliability estimation for drive axle of wheel loader under extreme small sample

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983684 ◽  
Author(s):  
Leilei Cao ◽  
Lulu Cao ◽  
Lei Guo ◽  
Kui Liu ◽  
Xin Ding
Keyword(s):  
Sample Size ◽  
Promising Result ◽  
Small Sample Size ◽  
Bootstrap Method ◽  
Estimation Method ◽  
Small Sample ◽  
Reliability Estimation ◽  
Fatigue Reliability ◽  
Drive Axle ◽  
Semi Empirical

It is difficult to have enough samples to implement the full-scale life test on the loader drive axle due to high cost. But the extreme small sample size can hardly meet the statistical requirements of the traditional reliability analysis methods. In this work, the method of combining virtual sample expanding with Bootstrap is proposed to evaluate the fatigue reliability of the loader drive axle with extreme small sample. First, the sample size is expanded by virtual augmentation method to meet the requirement of Bootstrap method. Then, a modified Bootstrap method is used to evaluate the fatigue reliability of the expanded sample. Finally, the feasibility and reliability of the method are verified by comparing the results with the semi-empirical estimation method. Moreover, from the practical perspective, the promising result from this study indicates that the proposed method is more efficient than the semi-empirical method. The proposed method provides a new way for the reliability evaluation of costly and complex structures.

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.

Application of the bootstrap method to quantify uncertainty in seismic hazard estimates

1992 ◽  
Vol 82 (1) ◽  
pp. 104-119
Author(s):  
Michéle Lamarre ◽  
Brent Townshend ◽  
Haresh C. Shah
Keyword(s):  
Confidence Interval ◽  
Seismic Hazard ◽  
Statistical Method ◽  
Bootstrap Method ◽  
Earthquake Magnitude ◽  
Earthquake Catalog ◽  
Uncertainty Measure ◽  
Attenuation Models ◽  
The Bootstrap Method

Abstract This paper describes a methodology to assess the uncertainty in seismic hazard estimates at particular sites. A variant of the bootstrap statistical method is used to combine the uncertainty due to earthquake catalog incompleteness, earthquake magnitude, and recurrence and attenuation models used. The uncertainty measure is provided in the form of a confidence interval. Comparisons of this method applied to various sites in California with previous studies are used to confirm the validity of the method.

Standard Error Estimation of 3PL IRT True Score Equating With an MCMC Method

2008 ◽  
Vol 33 (3) ◽  
pp. 257-278 ◽  
Author(s):  
Yuming Liu ◽  
E. Matthew Schulz ◽  
Lei Yu
Keyword(s):  
Bootstrap Method ◽  
Standard Errors ◽  
True Score ◽  
Mcmc Method ◽  
Test Form ◽  
True Score Equating ◽  
Standard Error Estimation ◽  
Equivalent Test ◽  
Mean Square Errors ◽  
The Bootstrap Method

A Markov chain Monte Carlo (MCMC) method and a bootstrap method were compared in the estimation of standard errors of item response theory (IRT) true score equating. Three test form relationships were examined: parallel, tau-equivalent, and congeneric. Data were simulated based on Reading Comprehension and Vocabulary tests of the Iowa Tests of Basic Skills®. For parallel and congeneric test forms within valid IRT true score ranges, the pattern and magnitude of standard errors of IRT true score equating estimated by the MCMC method were very close to those estimated by the bootstrap method. For tau-equivalent test forms, the pattern of standard errors estimated by the two methods was also similar. Bias and mean square errors of equating produced by the MCMC method were smaller than those produced by the bootstrap method; however, standard errors were larger. In educational testing, the MCMC method may be used as an additional or alternative procedure to the bootstrap method when evaluating the precision of equating results.

scholarly journals ACCURACY AND ERROR FACTORS OF SENSITOMETRIC CURVE USING THE BOOTSTRAP METHOD

1991 ◽  
Vol 47 (6) ◽  
pp. 811-817 ◽  
Author(s):  
AKIO OGURA ◽  
HIDEHARU NIIDA ◽  
KENICHI OGAWA ◽  
YOSHINORI KOMAI ◽  
HIDEHIKO TODOROKI ◽  
...  
Keyword(s):  
Bootstrap Method ◽  
The Bootstrap Method
Sign in / Sign up

Export Citation Format

Share Document