Use the delta method to estimate the variance of the maximum likelihood estimator of a function of the parameter(s).
Free SOA Exam ASTAM (Advanced Short-Term Actuarial Mathematics) lesson in Construction and Selection of Parametric Models. 21 min read, ~3,090 words.
MLE invariance: if is the MLE of, then is the MLE of, with no re-optimization. Univariate delta:, with both and the information evaluated at. Multivariate delta:, keeping off-diagonals, where is the inverse Fisher information (inverse Hessian of the negative log-likelihood). SE and CI: standard error is the square root of...
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What this lesson covers
- Content
- Example 1
- Example 2
- Example 3
- Common Mistakes
- Check Your Understanding
- Exam Shortcuts
Learning objectives
- 4c
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