= Absolute error bound for a ratio estimator with a controlled denominator
{title2=$\mathbb E|U_n/V_n-\theta|\le\delta^{-1}(|\mathbb EG_n|+\sqrt{\operatorname{Var}G_n})+r_n$}
Set $G_n=U_n-\theta V_n$, and define the estimator on zero-denominator events as part of the model. On $V_n>\delta>0$, its error is at most $|G_n|/\delta$. Centering $G_n$ and applying the <Cauchy-Schwarz inequality> gives the displayed bound, where $r_n$ is the expected error on $V_n\le\delta$. This controls a <ratio estimator> without falsely assuming that its numerator and denominator are independent.
Back to article page
