Manuscript En10-A@1 · En10-A.tex · section · 0a1d7743

A finite-shot allowance

Implementation tolerance on the same interface › A finite-shot allowance · lines 1239–1264

En10-A@1#eq:robust-shots

For a target radius $ε$ , the displayed certificate has a finite sufficient shot budget only when $b ε > δ$ , namely

n \geq ⌈ \frac{lo g ( 2/ α )}{2 ( b ε - δ ) ^{2}} ⌉ .

This is a limitation of this nominal certificate, not a universal impossibility theorem for alternative calibrated procedures.

If these assumptions hold conditional on calibration information and on an event $G$ with $Pr (G^{c}) \leq β$ , the same conditional proof followed by integration gives unconditional coverage at least $1 - α - β$ . The conditional independence and bias bounds must be justified; they do not follow from naming a device “calibrated”. This is the same statistical caution illustrated by the finite-confidence contracts in Oai265-B CheungOai265.

Displayed formulas in this passage

En10-A@1#eq:robust-shots · line 1244
$n \geq ⌈ \frac{lo g ( 2/ α )}{2 ( b ε - δ ) ^{2}} ⌉ .$

Nearby in this section

proposition: Proposition: Robust estimation under complete-channel error