Manuscript Psy04-A@1 · Psy04-A-v1.tex · corollary · d5800e2a

Corollary: Rectangular calibration allowance

Robust model and apparatus allowances › Complete-law stability · lines 1042–1068 · proof included or linked

Psy04-A@1#cor:calibration

Suppose simultaneous calibration gives

p \geq p_{-}, v \geq v_{-}, ϵ \leq ϵ_{+} < 1/2, η_{t} \geq η_{t, -} .

Set

A_{-} = p_{-} v_{-} (1 - 2 ϵ_{+}) t = 1 \prod^{T} η_{t, -} .

A sufficient robust gap is

\frac{1}{2} + \frac{A _{-}}{2 2} - e_{Q} - \frac{3}{4} - e_{C} .

For correlated calibration sets, rectangular enclosure is a conservative bound, not necessarily their exact optimum.

Proof. The retained advantage is nondecreasing in each nonnegative factor and nonincreasing in the assignment error. Use the simultaneous endpoints.

Displayed formulas in this passage

unlabeled · line 1045
$p \geq p_{-}, v \geq v_{-}, ϵ \leq ϵ_{+} < 1/2, η_{t} \geq η_{t, -} .$
unlabeled · line 1051
$A_{-} = p_{-} v_{-} (1 - 2 ϵ_{+}) t = 1 \prod^{T} η_{t, -} .$
unlabeled · line 1056
$\frac{1}{2} + \frac{A _{-}}{2 2} - e_{Q} - \frac{3}{4} - e_{C} .$