Parametric Bootstrap
Parametric Bootstrap Resampling · Also known as: parametrik bootstrap, model-based bootstrap, parametric resampling
The parametric bootstrap is a resampling method that estimates standard errors and confidence intervals by drawing repeated samples from a parametric model that has been fitted to the data. Developed in the bootstrap literature of Efron and Tibshirani (1993) and Davison and Hinkley (1997), it replaces analytic derivations for non-normal distributions and complex statistics.
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When to use it
Use the parametric bootstrap when you have a credible parametric model for the data and need standard errors or confidence intervals for a statistic whose sampling distribution is hard to derive analytically, especially under non-normal distributions or complex estimators. It does not require the data themselves to be normal, but it does require the model form to be correctly specified, and a sample of at least about 20 observations with B ≥ 1000 replications. With very small samples or a misspecified model the nonparametric bootstrap or a permutation test is safer.
Strengths & limitations
- Replaces hard or unavailable analytic standard-error derivations with simple simulation.
- Works for non-normal distributions and for complex statistics where closed-form formulas do not exist.
- Can be more efficient than the nonparametric bootstrap when the parametric model is genuinely correct, because it exploits the model structure.
- Results depend entirely on the assumed model form; if the model is misspecified the inference can be badly misleading.
- Unreliable in very small samples — below about 20 observations the nonparametric bootstrap is preferred, and below 10 a permutation test is safer.
- Requires a sufficient number of replications (B ≥ 1000), which adds computational cost.
Frequently asked
How is the parametric bootstrap different from the ordinary (nonparametric) bootstrap?
The nonparametric bootstrap resamples the observed data points with replacement, making no distributional assumption. The parametric bootstrap instead fits a parametric model to the data and simulates new samples from that fitted model. It can be more efficient when the model is correct, but misleading when the model is wrong.
How many replications do I need?
At least about 1000 replications (B ≥ 1000) are recommended so the simulated standard error and percentile interval are stable. More replications reduce the simulation noise at the cost of computation time.
What happens if my model is misspecified?
Because every simulated sample comes from the fitted model, a wrong model form propagates directly into the results and the intervals can be badly off. If you are unsure about the model, prefer the nonparametric bootstrap, which avoids this dependence.
What is the minimum sample size?
About 20 observations are recommended. Below 20 the nonparametric bootstrap is the safer choice, and below 10 a permutation test is preferred because parametric resampling becomes unreliable.
Sources
- Efron, B. & Tibshirani, R. J. (1993). An Introduction to the Bootstrap. CRC Press. ISBN: 978-0412042317
- Davison, A. C. & Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge University Press. ISBN: 978-0521574716
How to cite this page
ScholarGate. (2026, June 1). Parametric Bootstrap Resampling. ScholarGate. https://scholargate.app/en/statistics/parametric-bootstrap
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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