Re: Jackknife one step estimator?

tom wrote:
> X_1,X_2,...X_n are iid Bernoulli(p).
> the MLE of p^2 is ( (SUM 1 to n) X_i/n))^2. what is the jackknife
> estimator based on the MLE and how do i find it?


Look up the formula for the jackknife.

Each of the X's is either 0 or 1, so the R=(SUM 1 to n) X_i, then the
corresponding values for the psuedo-samples will be either R or R-1
(you probably need to work out how many of each there will be). Then
go on from there.

There is a well-known formula for an unbiased estimate of p^2 and you
might want to see if the jackknife estimator agrees with it, or is
close to it, as the jackknife estimator is meant to remove some bias
compared to an original estimate.


.

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