BCa Bootstrap F1 Confidence Interval Method

A BCa Bootstrap F1 Confidence Interval Method is a bias-corrected bootstrap confidence interval method that adjusts bootstrap percentiles using bias correction and acceleration parameters to improve coverage accuracy for skewed distributions.

• AKA: Bias-Corrected and Accelerated Bootstrap F1 CI, BCa F1 Interval Method, Adjusted Bootstrap F1 CI Method, Accelerated Bootstrap F1 Method.
• Context:
  • It can typically compute bias correction z₀ from proportion of bootstrap F1s < observed F1.
  • It can typically estimate acceleration parameter a from jackknife influence values.
  • It can typically adjust percentiles using Φ(z₀ + (z₀+zₐ)/(1-a(z₀+zₐ))) transformation.
  • It can often provide better coverage than simple percentile methods for skewed F1 distributions.
  • It can often handle transformation-respecting intervals that maintain range preservation.
  • It can often require more computation than basic bootstrap due to jackknife step.
  • It can range from being a Standard BCa Bootstrap F1 Confidence Interval Method to being a Smoothed BCa Bootstrap F1 Confidence Interval Method, depending on its percentile estimation.
  • It can range from being a Single-Level BCa Bootstrap F1 Confidence Interval Method to being a Multi-Level BCa Bootstrap F1 Confidence Interval Method, depending on its nesting structure.
  • It can range from being a Parametric BCa Bootstrap F1 Confidence Interval Method to being a Non-Parametric BCa Bootstrap F1 Confidence Interval Method, depending on its resampling model.
  • It can range from being a Fast BCa Bootstrap F1 Confidence Interval Method to being a Exact BCa Bootstrap F1 Confidence Interval Method, depending on its computational shortcuts.
  • ...
• Example(s):
  • Standard BCa Implementations, such as:
    • B=2000 bootstrap samples, n=50 observations.
    • Bias correction z₀=0.15, acceleration a=0.03.
    • Adjusted 95% CI: [0.72, 0.88] vs percentile [0.70, 0.86].
  • Skewed F1 Distributions, such as:
    • F1 near 0.95: Strong left skew, BCa shifts interval upward.
    • Basic percentile: [0.91, 0.97], BCa: [0.93, 0.98].
    • Better coverage for extreme values.
  • Comparison with Other Methods, such as:
    • Percentile: 91% coverage, BCa: 94.5% coverage (n=30).
    • Delta method: symmetric [0.75, 0.85], BCa: asymmetric [0.76, 0.87].
    • ABC method: similar coverage but 10x faster.
  • ...
• Counter-Example(s):
  • Basic Percentile Bootstrap Method, which uses raw percentiles.
  • Bootstrap-t Method, which uses variance estimates.
  • Delta-Method F1 Standard Error Estimation Method, which uses analytical approach.
• See: Bootstrap Method, Confidence Interval Method, Bias Correction, Acceleration Parameter, Jackknife Method, Bootstrap F1 Standard Error Estimation Method, Percentile Method, Skewed Distribution, Coverage Probability, Transformation-Respecting Interval, Non-Parametric Inference.

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