The bootstrap, why resampling your own data works

Question

You have n i.i.d. observations and a statistic \hat{	heta} (median, Sharpe ratio, a quantile, something without a friendly standard-error formula). Explain the bootstrap: the algorithm, why it works, and at least two situations where it fails.

Accepted Answer

The algorithm (nonparametric bootstrap). 1. From your sample x1, \dots, xn, draw n points with replacement, a "bootstrap sample." 2. Compute the statistic on it: \hat{	heta}^b. 3. Repeat B times (e.g., B = 10{,}000). 4. Use the spread of \{\hat{	heta}^1, \dots, \hat{	heta}^B\} as the sampling distribution: its standard deviation estimates the standard error; its quantiles give confidence intervals (percentile method, or better, bias-corrected variants). Why it works, the plug-in principle. The quantity you want is "the distribution of \hat{	heta} across samples of size n drawn from F," bu…

The bootstrap, why resampling your own data works

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