claimroutine

Coarse bin scale factor b/a

For b≥ab\ge a the first-channel scale factor is O(b/a)O(b/a)
coarse-bin case of the scale factor
Claim·§7.3 Mean comparisons and the cost of releasing a source·inside lemMean comparison scale factors and release cost

Statement (paper)

For b≥ab\ge a, the bound for the ssth-power norm of a first-channel mean contribution (its clipped relative error against 1+dy1+d_y) carries, on each child root-discrepancy power, the scale factor O(b/a)O(b/a). This follows from Equation  after conditional expectation and the mixture contraction of Lemma , with homogeneity giving a factor b/ab/a after division by aa. The factor f/πff/\pi_f in a product is bounded above and below by fixed constants, and for bounded nonnegative atoms a product-root difference splits into the factor-root differences multiplied by fixed constants times support indicators of the unaffected factor in one of the two versions.

In plain English

When b≥ab\ge a, the bound on the ssth-power norm of a first-channel mean contribution (its clipped relative error against 1+dy1+d_y) carries scale factor O(b/a)O(b/a) on each child root-discrepancy power.

Why it's here

This is the b≥ab\ge a case of the scale factor in the parent lemma. It follows from the relative-loss equation after conditional expectation and the mixture contraction in the estimation-loss lemma, with homogeneity supplying the b/ab/a after division by aa. Bounded f/πff/\pi_f factors and support indicators split product-root differences into factor-root differences, so no independence of the estimated factors is needed.
Classified routine:
A case of the parent lemma's scale-factor bound. It follows by conditional expectation, the mixture contraction of the estimation loss (lem-est-loss) and homogeneity, so it is bookkeeping on earlier nodes.

Uses

lemProperties of the estimation loss

Used by

claimSource-release cost f/u via incoming cap

Sources

PaperOpen
Section
§7.3 Mean comparisons and the cost of releasing a source
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sections/estimation.tex:249
Leannot aligned

Phase 2 aligns this node to a Lean declaration.