Manuscript Oai276-A@1 · Oai276-A.tex · proposition · 215068af

Proposition: Finite coverage is not an asymptotic rate

Stage 2: implementation, readout, and statistical pricing › Finite statistical coverage for a specified code · lines 1468–1489 · proof included or linked

Oai276-A@1#prop:statistics

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Let $Z_{N}$ be the mean of $N$ scores under Specification spec:statistics, with common expectation $s$ . Then

P {∣ Z_{N} - s ∣ > \frac{ln ( 2/ α )}{2 N}} \leq α .

If the intended and actual mean differ by at most $e$ , enlarge the interval by $e$ . A calibration-failure probability $β$ enlarges the total failure probability to at most $α + β$ .

Proof. Apply Hoeffding's inequality to independent variables in $[0, 1]$ , then the triangle inequality and a union bound Hoeffding.

Displayed formulas in this passage

unlabeled · line 1473
$P {∣ Z_{N} - s ∣ > \frac{ln ( 2/ α )}{2 N}} \leq α .$

Nearby in this section

assumption: Model specification: Complete attempted-run scoring
section: Finite statistical coverage for a specified code