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  • STA260 Lecture 08

Invariance Property of MLE

• Definition:

  • If $\hat{\theta }$ is the Maximum Likelihood Estimator (MLE) for $\theta$, then for any function $g(\theta )$, the MLE for $g(\theta )$ is $g(\hat{\theta })$.

• Context:

  • This property allows for the estimation of functions of parameters without re-deriving the likelihood maximization from scratch.

• Relation to Other Theorems:

  • Conceptually similar to the Continuous Mapping Theorem regarding the preservation of limits/convergence under continuous functions.

• Footnotes