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. 20 min read, ~2,927 words.
MLE invariance: if is the MLE of, then is the MLE of. No re-optimization needed. Univariate delta:, evaluated at. Multivariate delta:, where is the inverse Fisher information matrix. SE and CI: standard error is the square root of the delta-method variance; 95% Wald CI is. Validity: requires differentiable at with...
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- Example 1
- Example 2
- Example 3
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Learning objectives
- 4c
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