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Yunn-kuang Chu - One of the best experts on this subject based on the ideXlab platform.

  • Comparison on five estimation approaches of intensity for a queueing system with short run
    Computational Statistics, 2009
    Co-Authors: Yunn-kuang Chu
    Abstract:

    Traffic intensity is an important measure for assessing performance of a queueing system. In this paper, we propose a consistent and asymptotically normal estimator (CAN) of intensity for a queueing system with distribution-free interarrival and service times. Using this estimator and its estimated variance, a 100(1 − α )% asymptotic confidence interval of the intensity is constructed. Also, four Bootstrap approaches—standard Bootstrap, Bayesian Bootstrap, Percentile Bootstrap, and bias-corrected and accelerated Bootstrap are also applied to develop the confidence intervals of the intensity. A comparative analysis is conducted to demonstrate performances of the five confidence intervals of the intensity for a queueing system with short run data.

  • Analysis of intensity for a queueing system: Bootstrapping computation
    International Journal of Services Operations and Informatics, 2009
    Co-Authors: Yunn-kuang Chu
    Abstract:

    Traffic intensity plays an important role of system performance measures in queueing model. In this paper, we construct new confidence intervals of intensity for a queueing system, which are 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 perform the accuracy of these Bootstrap confidence intervals through calculating the coverage probability and the expected length of confidence intervals. Detailed discussions of the simulation results for four various types of queueing system are presented and some conclusions are provided. In addition, we demonstrate the four Bootstrap confidence intervals with a real-life example.

  • Bootstrapping comparison on availability of parallel systems with non‐identical components
    Engineering Computations, 2008
    Co-Authors: Yunn-kuang Chu, Jia‐huei Lee
    Abstract:

    Purpose – In order to develop a feasible and efficient method to acquire the long‐run availability of a parallel system with distribution‐free up and down times, the purpose of this paper is to perform the simulation comparisons on the interval estimations of system availability using four Bootstrapping methods.Design/methodology/approach – By using four Bootstrap methods; standard Bootstrap (SB) confidence interval, Percentile Bootstrap (PB) confidence interval, bias‐corrected Percentile Bootstrap (BCPB) confidence interval, and bias‐corrected and accelerated (BCa) confidence interval. A numerical simulation study is carried out in order to demonstrate performance of these proposed Bootstrap confidence intervals. Especially, we investigate the accuracy of the four Bootstrap confidence intervals by calculating the coverage percentage, the average length, and the relative coverage of confidence intervals.Findings – Among the four Bootstrap confidence intervals, the PB method has the largest relative covera...

  • Comparing confidence limits for short-run process incapability index Cpp
    Physica A: Statistical Mechanics and its Applications, 2008
    Co-Authors: Yunn-kuang Chu, Jer-yan Lin
    Abstract:

    Process incapability index Cpp has been proposed in the manufacturing industry to assess process incapability. In industries it is sometimes unable to get large samples, and, hence, the CAN (consistent and asymptotically normal) property of the unbiased estimator for Cpp is missing. In this paper, six Bootstrap methods are applied to construct upper confidence bounds (UCBs) of Cpp for short-urn production processes where sample size is small; standard Bootstrap (SB), Bayesian Bootstrap (BB), Bootstrap pivotal (BP), Percentile Bootstrap (PB), bias-corrected Percentile Bootstrap (BCPB), and bias-corrected and accelerated Bootstrap (BCa). A numerical simulation study is conducted in order to demonstrate the performance of the six various estimation methods. We further investigate the accuracy of the six methods by calculating the relative coverage (defined as the ratio of coverage percentage to average length of UCB). Detailed discussions of simulation results for seven short-run processes are presented. Finally, one real example from Ford Company’s Windsor Casting Plant is used to illustrate the six interval estimation methods.

  • COMPARATIVE ANALYSIS OF AVAILABILITY FOR A REDUNDANT REPAIRABLE SYSTEM
    Applied Mathematics and Computation, 2007
    Co-Authors: Yunn-kuang Chu
    Abstract:

    Abstract We consider the steady-state availability, denoted A , of a repairable system consisted of one operating unit and one spare. This paper we are interested in computational comparisons of confidence intervals for A based on four feasible and efficient approaches. The natural estimator A ^ of A , defined as the ratio of the sample mean lifetime of the operating unit to the sum of the sample mean lifetime of the operating unit and the sample mean downtime of system, is strongly consistent and asymptotically normal. The interval estimations for A are constructed through four Bootstrap approaches; standard Bootstrap confidence interval, Percentile Bootstrap confidence interval, bias-corrected Percentile Bootstrap confidence interval as well as bias-corrected and accelerated confidence interval. Finally, by calculating the coverage percentage and the average length of intervals, some numerical simulation comparisons are conducted in order to illustrate the performances of A ^ on various interval estimations.

Rand R. Wilcox - One of the best experts on this subject based on the ideXlab platform.

  • The Percentile Bootstrap: a primer with step-by-step instructions in R
    2019
    Co-Authors: Guillaume A Rousselet, Cyril R Pernet, Rand R. Wilcox
    Abstract:

    The Percentile Bootstrap is the Swiss Army Knife of statistics: it is a non-parametric method based on data-driven simulations. It can be applied to many statistical problems, as a substitute to standard parametric approaches, or in situations where parametric methods do not exist. In this tutorial, we cover R code to implement the Percentile Bootstrap in a few situations: one-sample estimation and the comparison of two independent groups for measures of central tendency (means and trimmed means) and spread. For each example, we explain how to derive a Bootstrap distribution, and how to get a confidence interval and a p value from that distribution. We also demonstrate how to run a simulation to assess the behaviour of the Bootstrap. In some situations, the Bootstrap performs poorly, such as when making inferences about the mean. But for other purposes, it is the only known method that works well over a broad range of situations, such as when comparing medians and there are tied (duplicated) values. More broadly, combining the Percentile Bootstrap with robust estimators, i.e. estimators that are not overly sensitive to outliers, the Bootstrap can help users gain a deeper understanding of their data, relative to conventional methods.

  • Comparing J independent groups with a method based on trimmed means
    Communications in Statistics - Simulation and Computation, 2017
    Co-Authors: A. Firat Özdemir, Rand R. Wilcox, Engin Yildiztepe
    Abstract:

    ABSTRACTThe ANOVA-F test is the most popular and commonly used procedure for comparing J independent groups. However, it is well known that this method is very sensitive to non-normality, which has led to the derivation of alternative techniques based on robust estimators. In this work, ANOVA-F-test, trimmed mean Welch test, Bootstrap-t trimmed mean Welch test, Schrader and Hettmansperger method with trimmed means, a Percentile Bootstrap method with trimmed means and a newly proposed method were compared in terms of both the Type I error probability and power. The proposed method compares well with ANOVA-F and other alternatives under various situations.

  • Global comparisons of medians and other quantiles in a one-way design when there are tied values
    Communications in Statistics - Simulation and Computation, 2016
    Co-Authors: Rand R. Wilcox
    Abstract:

    ABSTRACTFor J ⩾ 2 independent groups, the article deals with testing the global hypothesis that all J groups have a common population median or identical quantiles, with an emphasis on the quartiles. Classic rank-based methods are sometimes suggested for comparing medians, but it is well known that under general conditions they do not adequately address this goal. Extant methods based on the usual sample median are unsatisfactory when there are tied values except for the special case J = 2. A variation of the Percentile Bootstrap used in conjunction with the Harrell–Davis quantile estimator performs well in simulations. The method is illustrated with data from the Well Elderly 2 study.

  • Global comparisons of medians and other quantiles in a one-way design when there are tied values
    arXiv: Methodology, 2015
    Co-Authors: Rand R. Wilcox
    Abstract:

    For $J \ge 2$ independent groups, the paper deals with testing the global hypothesis that all $J$ groups have a common population median or identical quantiles, with an emphasis on the quartiles. Classic rank-based methods are sometimes suggested for comparing medians, but it is well known that under general conditions they do not adequately address this goal. Extant methods based on the usual sample median are unsatisfactory when there are tied values except for the special case $J=2$. A variation of the Percentile Bootstrap used in conjunction with the Harrell--Davis quantile estimator performs well in simulations. The method is illustrated with data from the Well Elderly 2 study.

  • Comparing Measures of Location: Some Small-Sample Results When Distributions Differ in Skewness and Kurtosis Under Heterogeneity of Variances
    Communications in Statistics - Simulation and Computation, 2012
    Co-Authors: A. Firat Özdemir, Rand R. Wilcox, Engin Yildiztepe
    Abstract:

    This article considers the problem of comparing two independent groups in terms of some measure of location. Nine methods, including a new method and a new robust estimator, were compared in terms of actual significance level and power. Simulations were performed using data generated from both theoretical distributions and data stemming from actual studies. For the theoretical distributions, the Bootstrap-t B 2 t method (with 20% trimming) and Yuen's test (with 10% trimming) performed best. Otherwise, the Bootstrap-t B 2 t method (with 25% trimming) and a Percentile Bootstrap method with trimmed means (20% and 25% trimming) or one-step M-estimator performed best.

Sidney J Segalowitz - One of the best experts on this subject based on the ideXlab platform.

  • statslab an open source eeg toolbox for computing single subject effects using robust statistics
    Behavioural Brain Research, 2018
    Co-Authors: Allan Campopiano, Stefon J R Van Noordt, Sidney J Segalowitz
    Abstract:

    Abstract Research on robust statistics during the past half century provides concrete evidence that classical hypothesis tests that rely on the sample mean and variance are problematic. Even seemingly minor departures from normality are now known to create major problems in terms of increased error rates and decreased power. Fortunately, numerous robust estimation techniques have been developed that circumvent the need for strict assumptions of normality and equal variances, leading to increased power and accuracy when testing hypotheses. Two robust methods that have been shown to have practical value across a wide range of applied situations are the trimmed mean and Percentile Bootstrap test. To facilitate the uptake of robust methods into the behavioural sciences, especially when dealing with trial-based data such as EEG, we introduce STATSLAB: An open-source EEG toolbox for computing single-subject effects using robust statistics. With the STATSLAB toolbox users can apply the Percentile Bootstrap test, with trimmed means, to a variety of neural signals including voltages, global field amplitude, and spectral features for both scalp channels and independent components. The toolbox offers a range of analytical strategies and is packaged with a fully functional graphical user interface that includes documentation.

Wilcox Rand - One of the best experts on this subject based on the ideXlab platform.

  • Global comparisons of medians and other quantiles in a one-way design when there are tied values
    2015
    Co-Authors: Wilcox Rand
    Abstract:

    For $J \ge 2$ independent groups, the paper deals with testing the global hypothesis that all $J$ groups have a common population median or identical quantiles, with an emphasis on the quartiles. Classic rank-based methods are sometimes suggested for comparing medians, but it is well known that under general conditions they do not adequately address this goal. Extant methods based on the usual sample median are unsatisfactory when there are tied values except for the special case $J=2$. A variation of the Percentile Bootstrap used in conjunction with the Harrell--Davis quantile estimator performs well in simulations. The method is illustrated with data from the Well Elderly 2 study.Comment: 18 pp. 2 figure

  • Inferences About the Skipped Correlation Coefficient: Dealing with Heteroscedasticity and Non-Normality
    DigitalCommons@WayneState, 2015
    Co-Authors: Wilcox Rand
    Abstract:

    A common goal is testing the hypothesis that Pearson’s correlation is zero and typically this is done based on Student’s T test. There are, however, several well-known concerns. First, Student’s T is sensitive to heteroscedasticity. That is, when it rejects, it is reasonable to conclude that there is dependence, but in terms of making a decision about the strength of the association, it is unsatisfactory. Second, Pearson’s correlation is not robust: it can poorly reflect the strength of the association. Even a single outlier can have a tremendous impact on the usual estimate of Pearson’s correlation, which can result in a poor indication of the strength of the association among the bulk of the points. Numerous robust correlation coefficients have been proposed that deal with outliers among the marginal distributions, but these methods do not take into account the overall structure of the data in terms of dealing with outliers. A skipped correlation addresses this concern and methods for testing the hypothesis that this correlation is zero have been studied. However, there are serious limitations associated with one of these methods and extant studies regarding an alternative Percentile Bootstrap method do not address practical concerns reviewed in the paper. A minor goal is to report situations where this Percentile Bootstrap method can be unsatisfactory. The main result is that an alternative Percentile Bootstrap method performs well in simulations

Allan Campopiano - One of the best experts on this subject based on the ideXlab platform.

  • statslab an open source eeg toolbox for computing single subject effects using robust statistics
    Behavioural Brain Research, 2018
    Co-Authors: Allan Campopiano, Stefon J R Van Noordt, Sidney J Segalowitz
    Abstract:

    Abstract Research on robust statistics during the past half century provides concrete evidence that classical hypothesis tests that rely on the sample mean and variance are problematic. Even seemingly minor departures from normality are now known to create major problems in terms of increased error rates and decreased power. Fortunately, numerous robust estimation techniques have been developed that circumvent the need for strict assumptions of normality and equal variances, leading to increased power and accuracy when testing hypotheses. Two robust methods that have been shown to have practical value across a wide range of applied situations are the trimmed mean and Percentile Bootstrap test. To facilitate the uptake of robust methods into the behavioural sciences, especially when dealing with trial-based data such as EEG, we introduce STATSLAB: An open-source EEG toolbox for computing single-subject effects using robust statistics. With the STATSLAB toolbox users can apply the Percentile Bootstrap test, with trimmed means, to a variety of neural signals including voltages, global field amplitude, and spectral features for both scalp channels and independent components. The toolbox offers a range of analytical strategies and is packaged with a fully functional graphical user interface that includes documentation.