Re: [S] Challenge: does a faster simple bootstrap algorithm exist?

Tim Hesterberg (timh@statsci.com)
Mon, 15 Jun 1998 08:24:24 -0700 (PDT)


>Here is a very fast algorithm for computing nonparametric
>confidence limits for the population mean using the basic
>bootstrap. ...

The algorithm gives the "bootstrap percentile interval",
i.e. percentiles of the bootstrap distribution.

The "basic bootstrap" confidence interval, in the terminology
of Davison & Hinkley 1997, is different, and corresponds to:

2*mean(x) - rev( quantile(z, c((1-conf.int)/2,(1+conf.int)/2)))

>Here x is a numeric vector of length n with no NAs present.
>conf.int is for example 0.95 and B is the number of boostrap
>reps (default B=1000)
>
>z <- unlist(lapply(1:B, function(i,x,N)
> sum(x[.Internal(sample.index(N, N, T),
> "S_sample",T,0)]), x=x, N=n)) / n
>quantile(z, c((1-conf.int)/2,(1+conf.int)/2))

The two methods handle asymmetry and bias in diametrically opposite
ways. Neither is particularly accurate. Alternatives include the
bootstrap-t and BCa intervals.

Tim Hesterberg
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