The Maximum Likelihood Estimator

$${\theta }_{MLE}=p(x;\theta )$$

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A popular alternative to BLUE.

It is based on the Likelihood Function

$$L(\theta |x)=p(x;\theta )$$

Where we try to find

$${\theta }_{MLE}={\text{argmax}}_{\theta }L(\theta |x)$$

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Asymptotic Properties of the MLE Invariance Property of the MLE