search for: d_n

Dear R-list members, Just wondering if there is any way to compute the duplication matrix in R. I tried to search for it but only found functions "xpnd" and "vech". Basically for a symmetric n by n matrix A, the duplication matrix D_n is a matrix of dimension n^2 by n(n+1)/2 such that D_n vech(A)= c(A), where c(A) just vectorizes A. The duplication matrix is defined on page 49 of the book "Matrix differential calculus with applications in statistics and econometrics" by Magnus and Neudecker (1988 ) Thanks a lot!...

.... (Also, I have now discovered, in stand-alone Fortran.) The phenomenon boils down to this: I generate ``nsam'' samples of chi-squared_1 iid random variables, each sample being of size ``n''. For each sample, let M be the maximum of the sample, and let the statistic S = (M - d_n)/2, where d_n = 2*ln(n) - ln(ln(n)) - ln(pi). Count the number K of times that G(S) < 0.05 where G(x) is the cdf of the Gumbel distribution, G(x) = exp(-exp(-x)). Then form alpha-hat = K/nsam. According to theory, alpha-hat should ---> 0.05 as n ---> infinity. (The chi-squared_...