Need a way to shorten and make code more effective - r

Question

I want to perform a bootstrap simulation 1000 times and compute percentile confidence intervals 1000 times for different samplesizes n = 10,20,...,100. I've solved this problem and I'm just asking, instead of doing this huge computations 10 times, covering 300 lines of code, is there a way to shorten this? Like, running this function over and over again 10 times? I tried a for-loop but it did not work. Here is the code that does work:
B = 1000 # number of replicates
kHat = Parameters[1] # approx = 2.06786
gammaHat = Parameters[2] # approx = 0.51144
TheoreticalMean = kHat/gammaHat
TheoreticalVariance = kHat/gammaHat^2
PercCoverage = vector("numeric", 10L)
n = 10 # sample size
getCI = function(B, k, gamma, n) {
getM = function(orgData, idx) {
bsM = mean(orgData[idx])
bsS2M = (((n-1) / n) * var(orgData[idx])) / n
c(bsM, bsS2M)
}
F = rgamma(n, kHat, gammaHat) # simulated data: original sample
M = mean(F) # M from original sample
S2M = (((n-1)/n)*var(F))/n # S^2(M) from original sample
# bootstrap
boots = t(replicate(B, getM(F, sample(seq(along=F), replace=TRUE))))
Mstar = boots[,1] # M* for each replicate
S2Mstar = boots[,2] # S^2*(M) for each replicate
biasM = mean(Mstar)-M # bias of estimator M
# indices for sorted vector of estimates
idx = trunc((B+1)*c(0.05/2,1-0.05/2))
ciPerc = sort(Mstar)[idx] # percentile CI
c(perc=ciPerc)
}
# 1000 bootstraps
Nrep <- 1000 # number of bootstraps
CIs <- t(replicate(Nrep, getCI(B, kHat, gammaHat, n)))
# coverage probabilities
PercCoverage[1] = sum((CIs[,"perc1"]<TheoreticalMean) & (CIs[,"perc2"]>TheoreticalMean)) / Nrep
However, here I need to script this for n=10, n=20 and so on to n=100, and each time I need to change PercCoverage[1] to PercCoverage[2]...PercCoverage[10] in order to store these values in an array for later plotting.
I tried setting n=c(10,20,30,40,50,60,70,80,90,100) and then placing all of the above in a for loop but the function getCI needed numerical value.
EDIT: For loop attempt:
n = c(10,20,30,40,50,60,70,80,90,100)
B = 1000 # number of replicates
kHat = Parameters[1] # approx = 2.06786
gammaHat = Parameters[2] # approx = 0.51144
TheoreticalMean = kHat/gammaHat
TheoreticalVariance = kHat/gammaHat^2
PercCoverage = vector("numeric", 10L)
for (i in length(n)){
getCI = function(B, k, gamma, n[i]) {
getM = function(orgData, idx) {
bsM = mean(orgData[idx])
bsS2M = (((n[i]-1) / n[i]) * var(orgData[idx])) / n[i]
c(bsM, bsS2M)
}
F = rgamma(n[i], kHat, gammaHat) # simulated data: original sample
M = mean(F) # M from original sample
S2M = (((n[i]-1)/n[i])*var(F))/n[i] # S^2(M) from original sample
# bootstrap
boots = t(replicate(B, getM(F, sample(seq(along=F), replace=TRUE))))
Mstar = boots[,1] # M* for each replicate
S2Mstar = boots[,2] # S^2*(M) for each replicate
biasM = mean(Mstar)-M # bias of estimator M
# indices for sorted vector of estimates
idx = trunc((B+1)*c(0.05/2,1-0.05/2))
ciPerc = sort(Mstar)[idx] # percentile CI
c(perc=ciPerc)
}
# 1000 bootstraps
Nrep <- 1000 # number of bootstraps
CIs <- t(replicate(Nrep, getCI(B, kHat, gammaHat, n[i])))
# coverage probabilities
PercCoverage[i] = sum((CIs[,"perc1"]<TheoreticalMean) & (CIs[,"perc2"]>TheoreticalMean)) / Nrep
}

Answer 1

Consider defining multiple functions: a master one boostrap_proc, gCI, and getM. Then pass in your sequences of sample sizes in lapply for list return or sapply for numeric vector each calling the master function and returning a series of probabilities (last line of function). Be sure to remove the hard coded n = 10.
Define Functions
B = 1000 # number of replicates
kHat = Parameters[1] # approx = 2.06786
gammaHat = Parameters[2] # approx = 0.51144
TheoreticalMean = kHat/gammaHat
TheoreticalVariance = kHat/gammaHat^2
bootstrap_proc <- function(n) {
Nrep <- 1000 # 1000 bootstraps
CIs <- t(replicate(Nrep, getCI(B, kHat, gammaHat, n)))
# coverage probabilities
sum((CIs[,"perc1"]<TheoreticalMean) & (CIs[,"perc2"]>TheoreticalMean)) / Nrep
}
getCI <- function(B, k, gamma, n) {
F <- rgamma(n, kHat, gammaHat) # simulated data: original sample
M <- mean(F) # M from original sample
S2M <- (((n-1)/n)*var(F))/n # S^2(M) from original sample
# bootstrap
boots <- t(replicate(B, getM(F, sample(seq(along=F), replace=TRUE),n)))
Mstar <- boots[,1] # M* for each replicate
S2Mstar <- boots[,2] # S^2*(M) for each replicate
biasM <- mean(Mstar)-M # bias of estimator M
# indices for sorted vector of estimates
idx <- trunc((B+1)*c(0.05/2,1-0.05/2))
ciPerc <- sort(Mstar)[idx] # percentile CI
c(perc=ciPerc)
}
getM <- function(orgData, idx, n) {
bsM <- mean(orgData[idx])
bsS2M <- (((n-1) / n) * var(orgData[idx])) / n
c(bsM, bsS2M)
}
Call Function
sample_sizes <- c(10,20,30,40,50,60,70,80,90,100)
# LIST
PercCoverage <- lapply(sample_sizes, bootstrap_proc)
# VECTOR
PercCoverage <- sapply(sample_sizes, bootstrap_proc)
# VECTOR
PercCoverage <- vapply(sample_sizes, bootstrap_proc, numeric(1))