Estimating odds and log odds with guaranteed accuracy

TL;DR

This paper introduces two unbiased estimators for odds and log odds from Bernoulli data that guarantee bounded relative error variance for all probabilities, ensuring reliable estimation.

Contribution

It proposes novel unbiased estimators for odds and log odds with guaranteed accuracy bounds applicable across all probability values.

Findings

Estimators are unbiased and have bounded variance relative to true values.

Guarantee of accuracy holds uniformly for all p in (0,1).

Estimators are near optimal per Wolfowitz's bound.

Abstract

Two sequential estimators are proposed for the odds p/(1-p) and log odds log(p/(1-p)) respectively, using independent Bernoulli random variables with parameter p as inputs. The estimators are unbiased, and guarantee that the variance of the estimation error divided by the true value of the odds, or the variance of the estimation error of the log odds, are less than a target value for any p in (0,1). The estimators are close to optimal in the sense of Wolfowitz's bound.