st: Problem in modifying built-in ktau.ado code (for Kendall's tau)

[Mike Lacy <Michael.Lacy@colostate.edu>]

Greetings,

I need to calculate Kendall's tau as efficiently as possible on two 
continuous variables for each repetition in a large set of bootstrap 
experiments. Calculating Kendall's tau is slow, being of order (N^2)/2. My 
estimate is that using the built-in ktau.ado command, which is the fastest 
command to obtain Kendall's tau in Stata, the bootstrap experiments will 
take at least 10-15 days of dedicated time on a fast Wintel machine.

Consequently, I am trying to modify the code of the ktau.ado into my own 
version.  In the middle of the loop in ktau.ado, I discovered there is a 
call to the sign() function, which accounts for about 70% of the execution 
time of ktau.ado.  My idea was to avoid the overhead of a function call by 
replacing the sign() function with an equivalent set of If statements.  So, 
I calculate my own "mysign" function value using Ifs and use it in place of 
sign() in the original code. However, I am not getting the right results, 
as I explain below after presenting the two relevant code fragments:

* Built-in ktau.ado code goes like this:
* View with a about a 10 pt nonproportional font
* `x' and `y' reference the two variables
* passed to the ktau command
gen double `work' = 0
scalar `k' = 2
while (`k' <= `N') {
   local kk = `k' - 1
   #delimit ;
   replace `work' = `work'
      + sign((`x' - `x'[`k'])*(`y' - `y'[`k'])) /* slow */
      in 1/`kk' ;
   #delimit cr
   scalar `k' = `k' + 1
}

Below is what I tried to do. And yes, I know that
if/else would be faster but I was trying to simplify
my code as much as possible while trying to track down
my error.

* My code, with differences  indicated
gen double `work' = 0
scalar `k' = 2
while (`k' <= `N') {
   local kk = `k' - 1
* Calc "mysign" as a substitute for the sign() function
* The rest of the code is as untouched as possible
  scalar pairprod = (`x' - `x'[`k'])*(`y' - `y'[`k']) in 1/`kk'
  if (pairprod < 0)  {scalar mysign = -1}
  if (pairprod > 0)  {scalar mysign =  1}
  if (pairprod == 0) {scalar mysign = 0}
  if (pairprod == .) {scalar mysign = .}
*
   #delimit ;
   replace `work' = `work'
      + mysign
   /* + sign((`x' - `x'[`k'])*(`y' - `y'[`k']))  Removed */
   in 1/`kk' ;
   #delimit cr
   scalar `k' = `k' + 1
}

Problem: I have checked the values of "mysign" vs. sign{) and they are the 
same for each iteration of the loop. However, at the end of the while loop, 
the values in the variable `work' are not what they should be, so I presume 
the problem is with what I have done with the "replace" command. Could 
someone offer some suggestion?

Thanks,


=-=-=-=-=-=-=-=-=-=-=-=-=
Mike Lacy
Fort Collins CO USA
(970) 491-6721 office





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