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Stat 5601 (Geyer) Examples (Subsampling Bootstrap)


General Instructions

To do each example, just click the "Submit" button. You do not have to type in any R instructions or specify a dataset. That's already done for you.

Time Series

Sections 8.5 and 8.6 in Efron and Tibshirani.


Extreme Values

Section 7.4 in Efron and Tibshirani.


Suppose X1, X2, . . ., Xn are independent and identically distributed Uniform(0, θ) random variables. Since the larger the sample the more the largest values crowd up against θ, the natural estimator of θ is the maximum data value X(n). This is in fact the maximum likelihood estimate.

The main statistical interest in this estimator is that it is a counter example to both the square root law and the usual asymptotics of maximum likelihood.

More precisely, (this was proved for homework in my theory class, Problem 10-4 in my lecture notes)

n (θ − X(n))
converges in distribution to the Exp(1 / θ) distribution.

But to use the subsampling bootstrap, we need only know that that the square root law fails and the actual rate is n.

External Data Entry

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