I’m trying to write a series of posts explaining, in laymen’s terms, statistical methods. Bootstrapping is one of my favorite techniques, something that isn’t necessarily in the common parlance among non statisticians.
Most people are probably familiar with the word bootstrap, as in pulling oneself up by their bootstraps, which means, basically, to use what you’ve got in order to make your way. That’s what statistical bootstrapping is. When we’re not confident about what our distribution is or we don’t have a method for determining the parameter confidence interval, we can take what we have, a sample, and assume the sample is the best estimate for your population, then resample the initial sample with replacement to generate a population distribution that can be used to estimate a confidence interval.
There are 4 commonly used bootstrapping methods for estimating confidence intervals.
- Standard -uses mean squared error to estimate interval. can be a good method if estimator of variance is not available.
- Percentile – simple method. estimate parameter using each new sample then take middle range of values (for desired 95%, take middle 95% of values. Can be bias and skewed.
- T-Pivot – requires a pivot quantity relating values. For example, the t distibution does not depend on the mean or variance, so t can be used as a pivot to estimate either. Best estimates if the pivot quantity exists.
- BCA – Corrects percentile method for bias and skew.
Bootstrapping is useful because it doesn’t assume anything about the distribution, unlike many common statistical tests, but it can give you useful estimates for the confidence intervals.