Coverage Performance of the Non-Central F-based and Percentile Bootstrap Confidence Intervals for Root Mean Square Standardized Effect Size in One-Way Fixed-Effects ANOVA

Background A highly publicized meta-analysis of 42 clinical trials comprising 27,844 diabetics ignited a firestorm of controversy by charging that treatment with rosiglitazone was associated with a “…worrisome…” 43% greater risk of myocardial infarction ( p =0.03) and a 64% greater risk of cardiovascular death ( p =0.06). Objective The investigators excluded 4 trials from the infarction analysis and 19 trials from the mortality analysis in which no events were observed. We sought to determine if these exclusions biased the results. Methods We compared the index study to a Bayesian meta-analysis of the entire 42 trials (using odds ratio as the measure of effect size) and to fixed-effects and random-effects analyses with and without a continuity correction that adjusts for values of zero. Results The odds ratios and confidence intervals for the analyses are summarized in the Table . Odds ratios for infarction ranged from 1.43 to 1.22 and for death from 1.64 to 1.13. Corrected models resulted in substantially smaller odds ratios and narrower confidence intervals than did uncorrected models. Although corrected risks remain elevated, none are statistically significant (*p<0.05). Conclusions Given the fragility of the effect sizes and confidence intervals, the charge that roziglitazone increases the risk of adverse events is not supported by these additional analyses. The exaggerated values observed in the index study are likely the result of excluding the zero-event trials from analysis. Continuity adjustments mitigate this error and provide more consistent and reliable assessments of true effect size. Transparent sensitivity analyses should therefore be performed over a realistic range of the operative assumptions to verify the stability of such assessments especially when outcome events are rare. Given the relatively wide confidence intervals, additional data will be required to adjudicate these inconclusive results.

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Analytic and bootstrap confidence intervals for the common-language effect size estimate

Methodology ◽

10.5964/meth.4495 ◽

2021 ◽

Vol 17 (1) ◽

pp. 1-21

Author(s):

Johnson Ching-Hong Li ◽

Virginia Man Chung Tze

Keyword(s):

Confidence Intervals ◽

Effect Size ◽

Sexual Compulsivity ◽

Common Language ◽

Bootstrap Confidence Intervals ◽

Effect Size Estimate ◽

Type 1 Error ◽

Size Estimate ◽

The Common

Evaluating how an effect-size estimate performs between two continuous variables based on the common-language effect size (CLES) has received increasing attention. While Blomqvist (1950; https://doi.org/10.1214/aoms/1177729754) developed a parametric estimator (q') for the CLES, there has been limited progress in further refining CLES. This study: a) extends Blomqvist’s work by providing a mathematical foundation for Bp (a non-parametric version of CLES) and an analytic approach for estimating its standard error; and b) evaluates the performance of the analytic and bootstrap confidence intervals (CIs) for Bp. The simulation shows that the bootstrap bias-corrected-and-accelerated interval (BCaI) has the best protected Type 1 error rate with a slight compromise in Power, whereas the analytic-t CI has the highest overall Power but with a Type 1 error slightly larger than the nominal value. This study also uses a real-world data-set to demonstrate the applicability of the CLES in measuring the relationship between age and sexual compulsivity.

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Snow depth mapping with unpiloted aerial system lidar observations: a case study in Durham, New Hampshire, United States

The Cryosphere ◽

10.5194/tc-15-1485-2021 ◽

2021 ◽

Vol 15 (3) ◽

pp. 1485-1500

Author(s):

Jennifer M. Jacobs ◽

Adam G. Hunsaker ◽

Franklin B. Sullivan ◽

Michael Palace ◽

Elizabeth A. Burakowski ◽

...

Keyword(s):

Root Mean Square Error ◽

Mean Square Error ◽

Confidence Intervals ◽

Root Mean Square ◽

Snow Depth ◽

Coniferous Forest ◽

Horizontal Resolution ◽

Absolute Difference ◽

Mean Square ◽

Mean Absolute Difference

Abstract. Terrestrial and airborne laser scanning and structure from motion techniques have emerged as viable methods to map snow depths. While these systems have advanced snow hydrology, these techniques have noted limitations in either horizontal or vertical resolution. Lidar on an unpiloted aerial vehicle (UAV) is another potential method to observe field- and slope-scale variations at the vertical resolutions needed to resolve local variations in snowpack depth and to quantify snow depth when snowpacks are shallow. This paper provides some of the earliest snow depth mapping results on the landscape scale that were measured using lidar on a UAV. The system, which uses modest-cost, commercially available components, was assessed in a mixed deciduous and coniferous forest and open field for a thin snowpack (< 20 cm). The lidar-classified point clouds had an average of 90 and 364 points/m2 ground returns in the forest and field, respectively. In the field, in situ and lidar mean snow depths, at 0.4 m horizontal resolution, had a mean absolute difference of 0.96 cm and a root mean square error of 1.22 cm. At 1 m horizontal resolution, the field snow depth confidence intervals were consistently less than 1 cm. The forest areas had reduced performance with a mean absolute difference of 9.6 cm, a root mean square error of 10.5 cm, and an average one-sided confidence interval of 3.5 cm. Although the mean lidar snow depths were only 10.3 cm in the field and 6.0 cm in the forest, a pairwise Steel–Dwass test showed that snow depths were significantly different between the coniferous forest, the deciduous forest, and the field land covers (p < 0.0001). Snow depths were shallower, and snow depth confidence intervals were higher in areas with steep slopes. Results of this study suggest that performance depends on both the point cloud density, which can be increased or decreased by modifying the flight plan over different vegetation types, and the grid cell variability that depends on site surface conditions.

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Bootstrap Confidence Intervals for Multilevel Standardized Effect Size

Multivariate Behavioral Research ◽

10.1080/00273171.2020.1746902 ◽

2020 ◽

pp. 1-21 ◽

Cited By ~ 1

Author(s):

Mark H. C. Lai

Keyword(s):

Confidence Intervals ◽

Effect Size ◽

Bootstrap Confidence Intervals

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

Symmetry ◽

10.3390/sym11040484 ◽

2019 ◽

Vol 11 (4) ◽

pp. 484 ◽

Cited By ~ 3

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.

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A note on coverage error of bootstrap confidence intervals for quantiles

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100071802 ◽

1993 ◽

Vol 114 (3) ◽

pp. 517-531 ◽

Cited By ~ 3

Author(s):

D. De Angelis ◽

Peter Hall ◽

G. A. Young

Keyword(s):

Confidence Intervals ◽

Present Note ◽

Normal Approximation ◽

Poor Performance ◽

Density Estimator ◽

Bootstrap Confidence Intervals ◽

Coverage Error ◽

Bootstrap Percentile ◽

Coverage Accuracy ◽

Percentile Bootstrap

AbstractAn interesting recent paper by Falk and Kaufmann[11] notes, with an element of surprise, that the percentile bootstrap applied to construct confidence intervals for quantiles produces two-sided intervals with coverage error of size n−½, where n denotes sample size. By way of contrast, the error would be O(n−1) for two-sided intervals in more classical problems, such as intervals for means or variances. In the present note we point out that the relatively poor performance in the case of quantiles is shared by a variety of related procedures. The coverage accuracy of two-sided bootstrap intervals may be improved to o(n−½) by smoothing the bootstrap. We show too that a normal approximation method, not involving the bootstrap but incorporating a density estimator as part of scale estimation, can have coverage error O(n−1+∈), for arbitrarily small ∈ > 0. Smoothed and unsmoothed versions of bootstrap percentile-t are also analysed.

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Accuracy in Parameter Estimation for the Root Mean Square Error of Approximation: Sample Size Planning for Narrow Confidence Intervals

Multivariate Behavioral Research ◽

10.1080/00273171.2011.543027 ◽

2011 ◽

Vol 46 (1) ◽

pp. 1-32 ◽

Cited By ~ 42

Author(s):

Ken Kelley ◽

Keke Lai

Keyword(s):

Parameter Estimation ◽

Root Mean Square Error ◽

Sample Size ◽

Mean Square Error ◽

Confidence Intervals ◽

Root Mean Square ◽

Mean Square ◽

Sample Size Planning

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On the Admissibility of Simultaneous Bootstrap Confidence Intervals

Symmetry ◽

10.3390/sym13071212 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1212

Author(s):

Xin Gao ◽

Frank Konietschke ◽

Qiong Li

Keyword(s):

Confidence Intervals ◽

Delta Method ◽

Lasso Regression ◽

Bootstrap Confidence Intervals ◽

Simultaneous Confidence Intervals ◽

Multiple Parameters ◽

Joint Inference ◽

Smoothed Bootstrap ◽

Bootstrap Approach ◽

Percentile Bootstrap

Simultaneous confidence intervals are commonly used in joint inference of multiple parameters. When the underlying joint distribution of the estimates is unknown, nonparametric methods can be applied to provide distribution-free simultaneous confidence intervals. In this note, we propose new one-sided and two-sided nonparametric simultaneous confidence intervals based on the percentile bootstrap approach. The admissibility of the proposed intervals is established. The numerical results demonstrate that the proposed confidence intervals maintain the correct coverage probability for both normal and non-normal distributions. For smoothed bootstrap estimates, we extend Efron’s (2014) nonparametric delta method to construct nonparametric simultaneous confidence intervals. The methods are applied to construct simultaneous confidence intervals for LASSO regression estimates.

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BOOTSTRAP CONFIDENCE INTERVALS FOR STEADY-STATE AVAILABILITY

Asia Pacific Journal of Operational Research ◽

10.1142/s021759590400031x ◽

2004 ◽

Vol 21 (03) ◽

pp. 407-419 ◽

Cited By ~ 9

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.

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