The random variable 𝜃ˆ_MLE has Asymptotic Distribution equivalent to 𝑁𝑜𝑟𝑚𝑎𝑙(𝜇=𝜃, 𝜎²=1/𝐼(𝜃)), where:

• 𝜃 - is the true unknown population parameter
• 𝜃ˆ_MLE - is the MLE estimate of 𝜃
• 𝑁𝑜𝑟𝑚𝑎𝑙 - is the normal distribution
• 𝜇 - is the normal distribution's mean
• 𝜎² - is the normal distribution's variance
• 𝐼(𝜃) - is the Fisher Information - Fisher Information Matrix of 𝜃

This normal distribution is 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

Using it to Estimate Standard Error of 𝜃ˆ_MLE

Given the information above, we can approximate the standard error (𝑆𝐸) of the MLE estimate 𝜃ˆ_MLE

• 𝑆𝐸ˆ(𝜃ˆ_MLE) = √[ 1/𝐼(𝜃) ]

where:

• 𝑆𝐸ˆ(𝜃ˆ_MLE) - is the Estimated Standard Error of random variable 𝜃ˆ_MLE
  

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