FRM Part I · FRM Exam Part I · Simulation and Bootstrapping
An analyst has a sample of 200 daily returns and wants to estimate the standard error of the sample median using the bootstrap. Which procedure correctly describes the standard bootstrap?
The bootstrap resamples the original data with replacement, using the same sample size, computes the statistic each time, and uses the standard deviation of those many statistics as the standard error. Without replacement, full-size draws would just reproduce the original sample.
- ADraw 200 observations with replacement from the original sample, compute the median, repeat many times, and take the standard deviation of the resulting mediansCorrect
- BDraw 200 observations without replacement from the original sample, compute the median, and repeat many times
- CDraw observations from a normal distribution fitted to the sample mean and variance, then compute the median once
- DSplit the sample into two halves of 100 and take the difference between the two medians
Explanation
The standard (iid) bootstrap resamples with replacement from the observed data, producing samples of the same size as the original. The statistic is computed for each resample, and the standard deviation of those statistics estimates its standard error. Sampling without replacement at full size would reproduce the original sample every time.
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