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Related Concept Videos

Bootstrapping01:24

Bootstrapping

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The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is...
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Confidence Intervals01:21

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
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Uncertainty: Confidence Intervals00:54

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
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Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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An R-Based Landscape Validation of a Competing Risk Model
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The automatic construction of bootstrap confidence intervals.

Bradley Efron1, Balasubramanian Narasimhan1

  • 1Department of Biomedical Data Sciences and Department of Statistics Stanford University.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|March 17, 2021
PubMed
Summary
This summary is machine-generated.

Standard confidence intervals lack accuracy. Bootstrap confidence intervals offer improved accuracy, and new algorithms automate their construction using the R package bcaboot for greater precision.

Keywords:
bca methodexponential familiesnonparametric intervalssecond-order accuracy

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Area of Science:

  • Statistics
  • Computational Statistics

Background:

  • Standard confidence intervals are widely used but can be inaccurate.
  • Bootstrap methods offer enhanced statistical accuracy.

Purpose of the Study:

  • To introduce novel algorithms for automating the construction of bootstrap confidence intervals.
  • To improve the accuracy and practical application of confidence intervals.

Main Methods:

  • Development of new algorithms for automated bootstrap interval construction.
  • Implementation of these algorithms in the R package bcaboot.
  • Theoretical description and practical examples of algorithm application.

Main Results:

  • Bootstrap confidence intervals provide second-order accuracy, a significant improvement over standard methods.
  • The new algorithms automate a complex process, reducing the need for specialized programming.
  • The bcaboot package makes these advanced methods accessible to users.

Conclusions:

  • Automated bootstrap intervals offer a more accurate and practical alternative to standard intervals.
  • The bcaboot R package facilitates the use of these advanced statistical techniques.
  • Computer-driven algorithms enhance the reliability of statistical inference.