How to calculate confidence interval using the “bootstrap function” in R

Question

I am trying to calculate the confidence interval in R. Due to some special reasons, I have to do it with the functions in \"bootstrap\" package.(which means I can\'t use th

Answer 1

You could do this by hand.

library(bootstrap) 
data('law')
names(law) <- tolower(names(law))

set.seed(1)
theta <- function(ind) cor(law[ind, 1], law[ind, 2], method = "pearson")
law.boot <- bootstrap(1:15, 1000, theta) 

ci1 <- qnorm(p=c(.025, .975), 
            mean=mean(law.boot$thetastar), 
            sd=sd(law.boot$thetastar))

Gives:

> ci1
[1] 0.5055894 1.0268053

Compared to bootstrap from the scratch:

set.seed(1)
FX <- function(x) with(x, cor(lsat, gpa))
boot <- replicate(1000, FX(law[sample(nrow(law), round(nrow(law)), 
                                     replace=TRUE), ]))

ci2 <- qnorm(p=c(.025, .975), 
            mean=mean(boot), 
            sd=sd(boot))

Gives:

> ci2
[1] 0.5065656 1.0298412

Thus ci1 and ci2 seem to be similar.

However, note: I've adapted the bootstrap to 1,000 repetitions. With just 100 repetitions the difference is naturally somewhat larger.

Note 2: My answer considers CIs as asked. However, probably it's more appropriate to use the percentiles. See the thothal's answer how to obtain them.