What is the delta method?

hard

Answer

$N(g({\theta}), \;g({\theta})^{2}\; \cdot \;\operatorname{Var}({\theta}))$
$Use to derive SE of transformations (ratios, log-odds).$
$\operatorname{Var}(\operatorname{log}(p))$
$Central for A/B testing ratio metrics (CTR per user, revenue per user with per-user denominator).$
$Fast alternative to bootstrap when you have a closed-form derivative.$

Check yourself — multiple choice

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$\operatorname{SE}(g({\theta}))$ ≈ |g'(θ)| · $\operatorname{SE}({\theta})$ ; used for ratios / log-odds / A/B ratio metrics — closed-form alt to bootstrap when derivative exists
Same as bootstrap
Only for MLE

Delta method: SE of g(θ̂) via g'(θ); central for ratio metrics.

#estimation#confidence-interval#ab-testing

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