[R] Theil test help

[KARSTEN G HOLMQUIST]

Hello,

I have a series of questions that I hope will be simple to answer.  Basically I would like a code to do the following so that I can compute the distribution free test for the slope of a postulated regression line (Theil test).  As I am testing the null hypothesis that slope = 0 against the general alternative the slope does not equal 0, it should be pretty straight-forward.

I have a data frame as follows;


index	Score	Mean_Temp	SD_Mean_Temp
i	10	3.7		0.65
i+1	12	7.5		2.11
i+2	6	10.3		0.85
...	...	...		...
n	8	12.6		4.2

The first question is how can I compute the n(n-1)/2 differences between Score i and Score j where i is from 1 to (n-1) and j is from (i+1) to n?  I would then like R to spit out the differences in a file something like the following;

i	j	Difference
1	2	2
1	3	-4
...	..	...
(n-1)	n	D(n-1,n)

The second question is for each indexed sample from i to n, I would like to use something like rnorm(n, mean = 0, sd = 1) so that I could generate 1000 random draws from the distribution specified so that the arguments for rnorm () are as follows; mean = the value of Mean_Temp & sd = SD_Mean_Temp for indexed values i to n.  I would, of course, then like R to spit out the massive table with 1000 columns of randomly generated temperature values for each index i to n.

Finally I would like to compute the slope estimator associated with the Theil statistic.  All I need to do is compute the n(n-1)/n individual slope values; Sij = (Yj -Yi)/(Xj-Xi) where the Ys are the Scores for samples i to n and the Xs are the set of randomly generated temperature values, as before, 1 less than or equal to i less than j less than or equal to n.  The median is then the estimator of Beta (the slope).  I would like to compute the slopes for all 1000 sets of randomly generated temperature values.

i would greatly appreciate any help with these questions

Sincerely,
karsten G Holmquist
USDA-ARS-VCRU