Bootstrap standard error from six resampled means

Question

You resample a batch of trade profits with replacement and recompute the average profit each time. For a small demonstration you keep six bootstrap replicates of the mean (in basis points):

$4, \quad 6, \quad 8, \quad 8, \quad 6, \quad 4.$

Estimate the bootstrap standard error of the mean profit.

Accepted Answer

The bootstrap standard error is the standard deviation of the replicate values (sample version, dividing by B - 1, with B = 6). Step 1, mean of the replicates. \bar{	heta}^ = \frac{4 + 6 + 8 + 8 + 6 + 4}{6} = \frac{36}{6} = 6. Step 2, squared deviations from 6. (-2)^2 + 0^2 + 2^2 + 2^2 + 0^2 + (-2)^2 = 4 + 0 + 4 + 4 + 0 + 4 = 16. Step 3, divide by B - 1 = 5 and take the square root. 	ext{SE}{	ext{boot}} = \sqrt{\frac{16}{5}} = \sqrt{3.2} \approx 1.79. For the mean you could also use the textbook standard error, but the bootstrap gets there too and, unlike the formula, keeps working for mes…

Bootstrap standard error from six resampled means

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