Nothing

```
EERpenalties <-
function(n, k = n - 1, m = min(n - 2, k), eer = .20, reps = 50000, rnd = 3){
if(!isTRUE(all.equal(n %% 4, 0))) stop("n must be a multiple of 4")
if(!isTRUE(all.equal(k %% 1, 0))) stop("k must be an integer")
if(!isTRUE(all.equal(m %% 1, 0))) stop("m must be an integer")
if(k > n - 1) stop("k cannot be greater than n-1")
if(k < 1) stop("k cannot be less than 1")
if(m > k) stop("m cannot be greater than k")
if(m < 1) stop("m cannot be less than 1")
if(m > (n - 2)) stop("m cannot be greater than n-2")
if(eer <= 0) stop("EER must be greater than 0")
if(eer >= 1) stop("EER must be less than 1")
# Algorythm callculates differences between penalties
# starting with diff(m-1) = pen(m) - pen(m-1)
cs <- NULL
startj <- m - 1
# The value of diff(m-1) can (under a certain condition) be calculated analytically.
if(qf((1 - eer / (k + 1 - m)), 1, (n - 1 - m)) > n - 1 - m){
cs <- log(qf((1 - eer / (k + 1 - m)), 1, (n - 1 - m)) / (n - 1 - m) + 1)
startj <- m - 2
}
# Stop if m=1 and diff(0) was calculated above.
if(startj < 0){
cs <- round(c(0, cs), rnd)
return(cs)
}
# Loop that estimates diff(j) for j = starj, startj-1, ... 1, 0.
# Estimate of diff(j) is based on assuming j large active effects.
for(j in startj:0){
# Create matrix of squared random N(0,1) observations.
# Number of columns is n-1-j which equals inactive columns (k-j) plus unused columns (n-1-k).
sqres<-matrix(rnorm(reps*(n-1-j))^2,reps,n-1-j)
# If there is more than one inactive column (k!=j+1) then sort entries for inactive columns.
# Inactive columns are the last (k-j) columns.
if((n - k) != (n - 1 - j)) sqres[ , (n - k):(n - 1 - j)] <- t(apply(sqres[ , (n - k):(n - 1 - j)], 1, sort))
# Find RSS for models containing just the j active effects, the j-effect model + 1, ... the j-effect model + m-j.
lRSS <- log(apply(sqres, 1, cumsum)[(n - m - 1):(n - 1 - j), ])
d1 <- dim(lRSS)[1]
# If d1==2 then m = j+1. In this case at most one variable is being added.
# The differences in log(RSS) are found and the relevant quantile taken to estimate diff(j).
if(d1 == 2){
out <- lRSS[2, ] - lRSS[1, ]
cs <- as.numeric(quantile(out, 1 - eer))
}
# If m> j+1 then the maximum number of additional variables is >=2.
# The models that add >=1 variable are compared and the one that will minimize
# APC* identified. For this model the difference in log(RSS) between this
# this model and the j-variable model plus its current penalty is recorded in out.
# The value of diff(j) that allows the specified EER to be achieved
# is estimated (newc) and the current list of penalties is updated.
if(d1 > 2){
out <- lRSS[d1, ] - apply((lRSS[-d1, ] + c(cs, 0)), 2, min)
newc <- quantile(out, 1 - eer)
cs <- c(cs + newc, newc)
}
}
cs <- round(c(0, cs[length(cs):1]), rnd)
attributes(cs) <- NULL
return(cs)
}
```

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