scholarly journals ON THE NUMBER OF BOOTSTRAP REPETITIONS FOR BCa CONFIDENCE INTERVALS

2002 ◽  
Vol 18 (4) ◽  
pp. 962-984 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Moshe Buchinsky
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
High Probability ◽  
Random Variables ◽  
American Statistical Association ◽  
Bootstrap Confidence Interval ◽  
Statistical Association ◽  
Step Method ◽  
Bootstrap Confidence Intervals ◽  
The Ideal

This paper considers the problem of choosing the number of bootstrap repetitions B to use with the BCa bootstrap confidence intervals introduced by Efron (1987, Journal of the American Statistical Association 82, 171–200). Because the simulated random variables are ancillary, we seek a choice of B that yields a confidence interval that is close to the ideal bootstrap confidence interval for which B = ∞. We specify a three-step method of choosing B that ensures that the lower and upper lengths of the confidence interval deviate from those of the ideal bootstrap confidence interval by at most a small percentage with high probability.

BOOTSTRAP CONFIDENCE INTERVALS FOR STEADY-STATE AVAILABILITY

2004 ◽  
Vol 21 (03) ◽  
pp. 407-419 ◽  
Author(s):  
JAE-HAK LIM ◽  
SANG WOOK SHIN ◽  
DAE KYUNG KIM ◽  
DONG HO PARK
Keyword(s):  
Steady State ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Average Length ◽  
Repairable System ◽  
Bootstrap Confidence Interval ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Methods ◽  
Percentile Bootstrap

Steady-state availability, denoted by A, has been widely used as a measure to evaluate the reliability of a repairable system. In this paper, we develop new confidence intervals for steady-state availability based on four bootstrap methods; standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap-t confidence interval, and bias-corrected and accelerated confidence interval. We also investigate the accuracy of these bootstrap confidence intervals by calculating the coverage probability and the average length of intervals.

scholarly journals Confidence Interval For An Unknown Mathematical Expectation Based On Weakly Related Observations

2021 ◽  
Vol 03 (05) ◽  
pp. 160-171
Author(s):  
Yusupov Farrukh ◽  
◽  
Khasanova Zukhra ◽  
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Mathematical Expectation ◽  
Random Variables ◽  
Weak Relationship

In this article, we construct confidence intervals for estimating the unknown mathematical expectation of weakly related random variables. To do this, we first define a weak relationship.

Accuracy assessment of the joint CloudSat-CALIPSO global cloud amount based on the bootstrap confidence intervals

2021 ◽  
Author(s):  
Andrzej Kotarba ◽  
Mateusz Solecki
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Spatial Resolution ◽  
Confidence Level ◽  
Accuracy Assessment ◽  
Cloud Amount ◽  
Radiation Budget ◽  
Bootstrap Confidence Intervals ◽  
Fine Spatial Resolution ◽  
Interval Width

<p>Vertically-resolved cloud amount is essential for understanding the Earth’s radiation budget. Joint CloudSat-CALIPSO, lidar-radar cloud climatology remains the only dataset providing such information globally. However, a specific sampling scheme (pencil-like swath, 16-day revisit) introduces an uncertainty to CloudSat-CALIPSO cloud amounts. In the research we assess those uncertainties in terms of a bootstrap confidence intervals. Five years (2006-2011) of the 2B-GEOPROF-LIDAR (version P2_R05) cloud product was examined, accounting for  typical spatial resolutions of a global grids (1.0°, 2.5°, 5.0°, 10.0°), four confidence levels of confidence interval (0.85, 0.90, 0.95, 0.99), and three time scales of mean cloud amount (annual, seasonal, monthly). Results proved that cloud amount accuracy of 1%, or 5%, is not achievable with the dataset, assuming a 5-year mean cloud amount, high (>0.95) confidence level, and fine spatial resolution (1º–2.5º). The 1% requirement was only met by ~6.5% of atmospheric volumes at 1º and 2.5º, while more tolerant criterion (5%) was met by 22.5% volumes at 1º, or 48.9% at 2.5º resolution. In order to have at least 99% of volumes meeting an accuracy criterion, the criterion itself would have to be lowered to ~20% for 1º data, or to ~8% for 2.5º data. Study also quantified the relation between confidence interval width, and spatial resolution, confidence level, number of observations. Cloud regime (mean cloud amount, and standard deviation of cloud amount) was found the most important factor impacting the width of confidence interval. The research has been funded by the National Science Institute of Poland grant no. UMO-2017/25/B/ST10/01787. This research has been supported in part by PL-Grid Infrastructure (a computing resources).</p>

scholarly journals A Classroom Approach to Illustrate Transformation and Bootstrap Confidence Interval Techniques Using the Poisson Distribution

2017 ◽  
Vol 6 (2) ◽  
pp. 42 ◽  
Author(s):  
Per Gösta Andersson
Keyword(s):  
Problem Solving ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Poisson Distribution ◽  
Learning Process ◽  
Bootstrap Confidence Interval ◽  
New Techniques ◽  
Teacher Student ◽  
Bootstrap Techniques ◽  
Interval Estimator

The Poisson distribution is here used to illustrate transformation and bootstrap techniques in order to construct a confidence interval for a mean. A comparison is made between the derived intervals and the Wald  and score confidence intervals. The discussion takes place in a classroom, where the teacher and the students have previously discussed and evaluated the Wald and score confidence intervals. While step by step  interactively getting acquainted  with new techniques,  the students will learn about the effects of e.g. bias and asymmetry and ways of dealing with such phenomena. The primary purpose of this teacher-student communication is therefore not to find the  best possible interval estimator for this particular case, but rather to provide a study displaying a teacher and her/his students interacting with each other in an efficient and rewarding way. The teacher has a strategy of encouraging the students to take initiatives. This is accomplished by providing the necessary background of the problem and some underlying theory after which the students are confronted with questions and problem solving. From this the learning process starts. The teacher has to be flexible according to how the students react.  The students are supposed to have studied mathematical statistics for at least two semesters. 

scholarly journals Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 484 ◽  
Author(s):  
Gadde Srinivasa Rao ◽  
Mohammed Albassam ◽  
Muhammad Aslam
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Process Capability ◽  
Real Data ◽  
Process Capability Index ◽  
Monte Carlo Simulation Study ◽  
Bootstrap Confidence Intervals ◽  
Capability Index ◽  
Coverage Probabilities ◽  
Percentile Bootstrap

This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) for Weibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index Cpkw over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.

scholarly journals The use of the bootstrap method for the assessment of investment effectiveness and risk – the case of confidence intervals estimation for the Sharpe ratio and TailVaR

2020 ◽  
Vol 1/2020 (13) ◽  
pp. 40-50
Author(s):  
Jarno Klaudia ◽  
◽  
Smaga Łukasz ◽  
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Stock Exchange ◽  
Bootstrap Method ◽  
Interval Estimation ◽  
Sharpe Ratio ◽  
Estimation Methods ◽  
Bootstrap Confidence Interval ◽  
Warsaw Stock Exchange ◽  
Confidence Interval Estimation

This paper is aimed at presenting application of bootstrap interval estimation methods to the assessment of financial investment’s effectiveness and risk. At first, we give an overview of various methods of bootstrap confidence interval estimation, i.e. bootstrap-t interval, percentile interval and BCa interval. Then, bootstrap confidence interval estimation methods are used to estimate confidence intervals for the Sharpe ratio and TailVaR of the Warsaw Stock Exchange sectoral indices. The results show that the bootstrap confidence intervals of different types are quite similarly positioned for each of the analysed index and measure. Taking into the account the locations of confidence intervals for both the Sharpe ratio and TailVaR, the real estate sector tends to be the most advantageous from the investor’s viewpoint.

Two-Condition Within-Participant Statistical Mediation Analysis: A Path-Analytic Framework

2019 ◽  
Author(s):  
Amanda Kay Montoya ◽  
Andrew F. Hayes
Keyword(s):  
Confidence Intervals ◽  
Indirect Effect ◽  
Mediation Analysis ◽  
Analytic Approach ◽  
Analytic Framework ◽  
Hypothesis Tests ◽  
Bootstrap Confidence Intervals ◽  
Complex Models ◽  
Path Analytic ◽  
Statistical Mediation Analysis

Researchers interested in testing mediation often use designs where participants are measured on a dependent variable Y and a mediator M in both of two different circumstances. The dominant approach to assessing mediation in such a design, proposed by Judd, Kenny, and McClelland (2001), relies on a series of hypothesis tests about components of the mediation model and is not based on an estimate of or formal inference about the indirect effect. In this paper we recast Judd et al.’s approach in the path-analytic framework that is now commonly used in between-participant mediation analysis. By so doing, it is apparent how to estimate the indirect effect of a within-participant manipulation on some outcome through a mediator as the product of paths of influence. This path analytic approach eliminates the need for discrete hypothesis tests about components of the model to support a claim of mediation, as Judd et al’s method requires, because it relies only on an inference about the product of paths— the indirect effect. We generalize methods of inference for the indirect effect widely used in between-participant designs to this within-participant version of mediation analysis, including bootstrap confidence intervals and Monte Carlo confidence intervals. Using this path analytic approach, we extend the method to models with multiple mediators operating in parallel and serially and discuss the comparison of indirect effects in these more complex models. We offer macros and code for SPSS, SAS, and Mplus that conduct these analyses.

Sign in / Sign up

Export Citation Format

Share Document