For multinomial probabilities = ( 1 , 2 ,......) with a contingency table of arbitrary dimensions, suppose that a measure g() = /.

For multinomial probabilities π = (π₁, π₂,......) with a contingency table of arbitrary dimensions, suppose that a measure g(π) = ν/δ. Show that the asymptotic variance of √n [g(π̂) – g(π)] is σ² = [∑_i π_i η²_i – (∑_i π_i η_i)²]/δ⁴, where η_i = δ(∂ν/∂π_i) – ν(∂δ/∂π_i) (Goodman and Kruskal, 1972).