Parametric Bootstrap

The parametric bootstrap is an approximation to the sampling distribution. It can be used to get estimates for confidence intervals, etc.

Algorithm:

1. Identify estimators and point estimates from the data (AKA $\hat{\theta }$ - probably the Maximum Likelihood Estimator (MLE))
2. Generate n samples from the the proposed distribution using the point estimate of the parameter - sample from $f(Y|\hat{\theta })$
3. Compute estimates of parameters for each of the samples to make the bootstrap distribution
4. Use the bootstrap distribution for your conclusions

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References

@efron1994 - Pages 53-56 @rice2007 - Chapter 8