6.24 (Messig and Strawderman 1993) Show that for the general dose-response model p (x) = m i=1...

6.24 (Messig and Strawderman 1993) Show that for the general dose-response model pθ (x) = m i=1

ni xi



[ηθ (di)]

xi [1 − ηθ (di)]

ni−xi , the statistic X = (X1, X2,...,Xm) is minimal sufficient if there exist vectors

θ1, θ2, ··· , θm) such that the m × m matrix P =



log

ηθj (di)

1 − ηθ0 (di)

!

ηθ0 (di)

1 − ηθj (di)

!



is invertible. (Hint: Theorem 6.12.)