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Inferential Statisticshard
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Suppose we have a sample X1,...,XnX_1, ..., X_nX1​,...,Xn​ from a distribution with density f(x∣θ)f(x|\theta)f(x∣θ). The Fisher information I(θ)I(\theta)I(θ) is defined as E[(∂∂θln⁡f(X∣θ))2]E[(\frac{\partial}{\partial \theta} \ln f(X|\theta))^2]E[(∂θ∂​lnf(X∣θ))2]. If the model is misspecified, the 'Godambe information' is used. What is the standard structure of the Godambe information G(θ)G(\theta)G(θ)?