A confidence interval for the median with no formula

Question

You have 200 daily P&L numbers and want a 95% confidence interval for their median (not the mean, because P&L is fat-tailed and skewed). The median has no simple standard-error formula.

Describe how to get the interval by bootstrapping, why it works, and one pitfall.

Accepted Answer

Why not a formula. The standard error of the sample median depends on the density of the population at the median, an unknown quantity that ordinary summary statistics do not give you. So the clean "estimate ± 1.96 × SE" route is blocked. Resampling sidesteps the need for any formula. The bootstrap procedure. 1. From your 200 observations, draw a resample of 200 points with replacement. 2. Compute the median of that resample. 3. Repeat many times, say B = 10{,}000, collecting 10{,}000 bootstrap medians. 4. The 2.5th and 97.5th percentiles of those bootstrap medians form the 95% percentile con…

A confidence interval for the median with no formula

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