Let's say I figured out that the MLE of $\theta$ is $\hat\theta = \sqrt[n] {\frac{k}{n} - 1}$.
What is the MLE of $1 - \theta$?
Is it $1-\hat\theta$?
What is the MLE of $1 - \theta$ if the MLE of $\theta$ is already known
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statistics
statistical-inference
1 Answers
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Yes, the function $g: \mathbb{R} \to \mathbb{R}$ defined by $g(x) = 1-x$ is one-to-one, so by the invariance property of MLEs, the MLE of $1-\theta$ is $1-\hat{\theta}$.