7.7. Using the multivariate version of the delta method (Bishop et al. 1975, p.

493), show that the sample mean ridits Ä = ( Ä i , . . . , Är_i)' in a r x c table have asymptotic covariance matrix ¼'¸¼/ç, where Ó/ç is the re x re multinomial-based covariance matrix for the sample proportions [with Wai(pij) = nij(l-Kij)/n and Co\(pu, pu) = -ðß}ðÇ/ç] and D' is a

(r — 1) x re matrix with elements dAk dnn

\-CLj\k, _ i ^ k 1—á/É,-Ç , é = k,

ð,·+

with aj\k = Ó<<, Ki\k + (^j\k/2). Here A contains only r — 1 of the r sample mean ridits because of the linear constraint J2i Pi+^i — 0.50.