Burnside 1994 test

[lzjdsn]

Dear Tom,

I was studying the @Burnside procedure provided by RATS examples. Thank you for all of these fantastic and helpful examples.

I have a question about the @Burnside procedure. In the original paper, the authors calculated the Z1 statistic as Z1 = sqrt(T) * q / sigma(q). In the @Burnside procedure (please see below), the sqrt(T) is not in the formula for %cdstat. When I calculate the Z1 statistic, should I multiply %cdstat by sqrt(T) or the sqrt(T) has already embedded in the %cdstat formula in the @Burnside procedure?

Thank you for your help!



dim gap(nlist)
ewise gap(i)=1-mum*mur(i)
compute siggap=inv(sigr)*gap
compute q1=sqrt(%qform(inv(sigr),gap))
compute q=sqrt(sigm)-q1
compute [vector] deltam=||(1/q1)*%dot(mur,siggap),.5/sqrt(sigm)||
compute [vector] deltar=(1/q1)*mum*siggap
compute [symm] dsigma=((.5/q1)*siggap*tr(siggap))
compute deltah=%blockglue(||deltam|deltar|%vec(dsigma)||)
compute vq=%qform(%xx,deltah)
compute %cdstat=q/sqrt(vq)

[TomDoan]

If you look at his description, I would imagine that he's using X'X/T in his formulas (which would have an asymptotic limit) where we're using just X'X in the calculations. If you track through the powers of T, you'll see that you end up with the same test statistic.