This property is called asymptotic efficiency. I(θ) = −E [ ∂2 ∂θ2 ln L(θ|X) ] . Thus, the estimate of the variance given data x ˆσ2 = −1 / ∂2 ∂θ2 ln L(ˆθ|x). the negative reciprocal of the second derivative, also known as the curvature, of the log-likelihood function evaluated at the MLE.