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I am asked to conduct a Monte Carlo study to estimate the coverage probabilities of the standard normal bootstrap confidence interval, the basic bootstrap confidence interval, and the percentile confidence interval.

I am using the following code:

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B    <- 100                 # number of replicates
mu   <- 1                   # for generating data: true mean
sd   <- 1                   # for generating data: true sd
Data <- rnorm(N, mu, sd)    # simulated data: original sample


getM <- function(orgDV, idx) 
  {bsM  <- mean(orgDV[idx])                       # M*
  bsS2M <- (((N-1) / N) * var(orgDV[idx])) / N    # S^2*(M)
  c(bsM, bsS2M)
}

library(boot)                   # for boot(), boot.ci(), R=50 bootstrap replicates
bOot = boot(Data, statistic=getM, R=50)
boot.ci(bOot, conf=0.95, type=c("basic", "perc"))

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I need to "wrap" this into a function that generates a vector with bootstrap confidence intervals so that I can further determine the proportion of times that the confidence intervals miss on the left, and the proportion of times that the confidence intervals miss on the right.

I am a novice to R programming and played around with some "for loops" without success. Can you direct me to where I need to go.

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You may get better answers on stackoverflow, as this question relates more to programming than statistics.

It's not completely clear what you would like the code to produce, since a vector is 1 dimensional, so you could hold 1 item in the vector for each bootstrap confidence interval - but the information you want includes more than 1 thing - the type, the confidence level, the upper bound and the lower bound etc. So one simple way to do this is to use a list and enclose your code in a for loop, and add the object (which is in fact another list) returned by boot.ci like this:

require(boot)                   # for boot(), boot.ci()

N <-100
B    <- 100                 # number of replicates
mu   <- 1                   # for generating data: true mean
sd   <- 1                   # for generating data: true sd

getM <- function(orgDV, idx) 
    {bsM  <- mean(orgDV[idx])                       # M*
    bsS2M <- (((N-1) / N) * var(orgDV[idx])) / N    # S^2*(M)
    c(bsM, bsS2M)
}

N.CI <- 10             # number of botstrap confidence intervals
list.CI <- list(N.CI)  # a list to hold the objects returned by boot.ci

for (i in 1:N.CI ) {

    Data <- rnorm(N, mu, sd)    # simulated data: original sample
    bOot = boot(Data, statistic=getM, R=50)
    list.CI[[i]] <- boot.ci(bOot, conf=0.95, type=c("basic", "perc"))
}

list.CI now contains 10 boostrap confidence intervals. You can access each one by list.CI[[1]], list.CI[[2]] etc, and then you can access the components of each CI like this:

> list.CI[[i]]$perc
         conf                              
    [1,] 0.95 1.28 49.73 0.7794841 1.318904
> list.CI[[i]]$basic
    conf                              
[1,] 0.95 49.73 1.28 0.7980327 1.337453

Perhaps a better way, which will help your subsequent analysis is to store the bootstrap CIs in a matrix or a dataframe instead of a list, but I'll leave that for you to do.

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