 Absolute error bound for a ratio estimator with a controlled denominator

ID: absolute-error-bound-for-a-ratio-estimator-with-a-controlled-denominator

G_{n} = U_{n} - θ V_{n}

, and define the estimator on zero-denominator events as part of the model. On

V_{n} > δ > 0

, its error is at most

∣ G_{n} ∣/ δ

. Centering

G_{n}

and applying the Cauchy-Schwarz inequality gives the displayed bound, where

r_{n}

is the expected error on

V_{n} \leq δ

. This controls a ratio estimator without falsely assuming that its numerator and denominator are independent.

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