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Also known as: Bootstrap Resampling
Resampling with replacement from observed data to estimate variability, bias, and confidence intervals for statistics.
DESCRIPTION
The bootstrap approximates the sampling distribution by repeatedly resampling the observed data with replacement. It provides standard errors and confidence intervals without strong parametric assumptions. Variants include percentile, basic, and bias-corrected and accelerated (BCa) intervals. The approach is widely used when analytic variance formulas are unavailable or complex. Computational cost is manageable with modern hardware and parallelization. Introduced by Efron, the bootstrap revolutionized nonparametric inference.
ALTERNATIVE DEFINITIONS
Wikipedia
In statistics, bootstrapping is any test or metric that relies on random sampling with replacement.
Defines bootstrap broadly as resampling with replacement for inference.
NIST
The bootstrap is a method for estimating the distribution of a statistic by resampling with replacement from the sample data.
Emphasizes estimating a statistic’s distribution via resampling.
StatLect
The bootstrap estimates the sampling distribution of a statistic by repeatedly drawing bootstrap samples from the empirical distribution.
Highlights empirical distribution as the resampling source.
RELATED TERMS
Cross-Validation Confidence Interval Systematic Error Variance Empirical Distribution Percentile Method Monte Carlo Data Nonparametric Methods Resampling
COMPETING TERMS
Jackknife Bayesian Bootstrap
RELATIONS
- Broader: Nonparametric Methods Resampling
KNOWLEDGE AREAS
TARGET AUDIENCE
EXTERNAL SOURCES
- Wikipedia - Bootstrapping (statistics)
- NIST - NIST handbook section on bootstrap
- arXiv - Review of bootstrap methods
- StatLect - Bootstrap tutorial and examples
TOP QUESTIONS
What is the Bootstrap in statistics?
It’s a resampling method using replacement to approximate the sampling distribution of a statistic and compute standard errors and confidence intervals.
Category: Definition
Why use the Bootstrap?
It avoids strong parametric assumptions and works when exact formulas are hard or impossible, providing flexible uncertainty estimates.
Category: Relevancy
What are common Bootstrap interval types?
Percentile, basic, and BCa intervals. BCa often improves coverage by correcting bias and skewness.
Category: Example
What mistakes occur with the Bootstrap?
Small samples, heavy dependence, or non-representative data can mislead. Misusing percentile intervals for skewed distributions is common.
Category: Mistakes
How many Bootstrap resamples should I use?
Hundreds to thousands are typical; more improve stability. Balance computational cost and precision.
Category: Requirements
What is the Bayesian Bootstrap?
A Bayesian analogue assigning random weights from a Dirichlet distribution, offering a different uncertainty perspective.
Category: Alternatives
Does Bootstrap work for time series?
Yes, with block bootstrap or circular bootstrap to respect dependence. Naive resampling can break autocorrelation.
Category: Application
How does Bootstrap compare to Jackknife?
Bootstrap typically gives better variance estimates and flexibility, while Jackknife is simpler and less computationally intensive.
Category: Alternatives
What’s a striking analogy for Bootstrap?
Like making many synthetic datasets by reusing the same ingredients, to understand how a recipe’s outcome varies.
Category: Example