Bootstrap Confidence Interval

There are three main methods of constructing Bootstrap confidence interval.

  • Normal Interval
  • Pivotal Interval
  • Percentile Interval

Normal Interval

The normal confidence interval is defined as
Tn ± zα/2boot
where sêboot is the bootstrap estimate of standard error.

Pivotal Interval

Let θ = T(F) and θ̂ = T(F̂). Let θ̂*n,1, . . . , θ̂*n, 1 denote bootstrap replication of θ̂n.

The 1 – α bootstrap pivotal confidence interval is
Cn = (2θ̂n – θ̂*1 -α/2 , 2θ̂n – θ̂*α/2)

Percentile Interval

The Bootstrap percentile interval is defined by
Cn =(θ̂*α/2, θ̂*1 -α/2)

Bootstrap Example

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