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

 

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