Bootstrap estimate of Standard Error

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Definition: Bootstrap estimate of Standard Error

Bootstrap estimate is the method for calculating measures of accuracy to sample estimates. Bootstrap estimate falls under the category of re-sampling methods.

Bootstrap is used for estimating standard errors, biases and to calculate intervals of any statistics.

Method:

Let the given Data be “x”.

A Bootstrap sample is a random sample of size “a” taken with replacement from “x”

x* = (x1*, x2*,x3*,x4*,x5*…………..xa*)

Then, Bootstrap Replication:

of statistics Ê = s (x) is

Ê* = s (x*)

So, Bootstrap estimate of Standard Error is the observed standard deviation of repeated bootstrap replication.

Application:

• When the theoretical distribution of statistics of interest is unknown
• When the sample size is insufficient
• When power calculation has to be done and a small data is available

Hence, this concludes the definition of Bootstrap estimate of Standard Error along with its overview.

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