Beginning with the canonical coordinate system introduced at (8.17), transform from to with components r = Kr () + r,s,tu s t u/2

Beginning with the canonical coordinate system introduced at (8.17), transform from θ to ϕ with components

ϕr = Kr (θ) + νr,s,tuθ

sθ

tθ

u/2 + νr,s,tuθ

sν

t,u/2.

Show that, although E(Ur

; θ) ≠ ϕr

, nevertheless ϕˆr = Ur. Show also that the observed information determinant with respect to the components of ϕ satisfies 1

2 log det K∗rs (u; θˆ) =

1 2

log det ˆj rs

ϕ + νr,s,tuν

r,sν

t,u at the maximum likelihood estimate. Hence deduce (8.23) directly from (8.20).