Fisher Information Matrix of Asymptotic Distribution of the MLE

• 𝐼(𝜃) = 1/𝜎²

The Asymptotic Distribution of the MLE is a normal distribution governed by 𝜎² = 1/𝐼(𝜃):

• the larger the Fisher information 𝐼(𝜃), the smaller the variance 𝜎² of the normal distribution
• the smaller the Fisher Information 𝐼(𝜃), the larger the variance 𝜎² of the normal distribution

Resources