[R] Help with efficient double sum of max (X_i, Y_i) (X & Y vectors)

[Jeffrey Racine]

Greetings.

For R gurus this may be a no brainer, but I could not find pointers to
efficient computation of this beast in past help files.

Background - I wish to implement a Cramer-von Mises type test statistic
which involves double sums of max(X_i,Y_j) where X and Y are vectors of
differing length.

I am currently using ifelse pointwise in a vector, but have a nagging
suspicion that there is a more efficient way to do this. Basically, I
require three sums:

sum1: \sum_i\sum_j max(X_i,X_j)
sum2: \sum_i\sum_j max(Y_i,Y_j)
sum3: \sum_i\sum_j max(X_i,Y_j)

Here is my current implementation - any pointers to more efficient
computation greatly appreciated.

  nx <- length(x)
  ny <- length(y)

  sum1 <- 0
  sum3 <- 0
    
  for(i in 1:nx) {
    sum1 <- sum1 + sum(ifelse(x[i]>x,x[i],x))
    sum3 <- sum3 + sum(ifelse(x[i]>y,x[i],y))
  }

  sum2 <- 0
  sum4 <- sum3 # symmetric and identical
    
  for(i in 1:ny) {
    sum2 <- sum2 + sum(ifelse(y[i]>y,y[i],y))
  }

Thanks in advance for your help.

-- Jeff

-- 
Professor J. S. Racine         Phone:  (905) 525 9140 x 23825
Department of Economics        FAX:    (905) 521-8232
McMaster University            e-mail: racinej at mcmaster.ca
1280 Main St. W.,Hamilton,     URL:
http://www.economics.mcmaster.ca/racine/
Ontario, Canada. L8S 4M4

`The generation of random numbers is too important to be left to chance'