Manuscript Oai265-B@2 · Oai265-B-v2.tex · section · 94b6f42f

All-pass sample allowance

Exact binomial alternatives › All-pass sample allowance · lines 846–866

Oai265-B@2#eq:cpSamples

With $n$ passes out of $n$ in every setting,

p_{j, L} = ζ^{1/ n}, F_{L} = [1 - \frac{3}{2} (1 - ζ^{1/ n}) - b_{cal}]_{[0, 1]} .

For $q$ in (eq:samples), $0 < q < 3/2$ , acceptance of the exact binomial endpoints on all-pass data requires

n \geq \frac{lo g ( 6/ α _{s} )}{- lo g ( 1 - 2 q /3 )} .

The integer sample allowance is the ceiling. For small $q$ , this is of order $q^{- 1}$ , compared with the Hoeffding allowance of order $q^{- 2}$ . This comparison concerns favorable all-pass datasets.

Displayed formulas in this passage

Oai265-B@2#eq:cpSamples · line 857
$n \geq \frac{lo g ( 6/ α _{s} )}{- lo g ( 1 - 2 q /3 )} .$
unlabeled · line 849
$p_{j, L} = ζ^{1/ n}, F_{L} = [1 - \frac{3}{2} (1 - ζ^{1/ n}) - b_{cal}]_{[0, 1]} .$