For multinomial probabilities = ( 1 , 2 ,......) with a contingency table of arbitrary
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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 πi η2i – (∑i πi ηi)2]/δ4, where ηi = δ(∂ν/∂πi) – ν(∂δ/∂πi) (Goodman and Kruskal, 1972).
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