Estimation of a Probability with Guaranteed Normalized Mean Absolute Error

TL;DR

This paper presents a sequential estimation method for a probability in Bernoulli trials, providing formulas and bounds for the mean absolute error to ensure accurate probability estimation with a guaranteed normalized error level.

Contribution

It introduces a simple stopping rule and derives closed-form expressions and bounds for the mean absolute error of the estimator, enabling controlled probability estimation.

Findings

Derived closed-form expression for mean absolute error

Established upper bounds for estimation error

Enabled probability estimation with guaranteed normalized error

Abstract

The estimation of a probability p from repeated Bernoulli trials is considered in this paper. A sequential approach is followed, using a simple stopping rule. A closed-form expression and an upper bound are obtained for the mean absolute error of the unbiased estimator of p. The results given permit the estimation of an arbitrary probability with a prescribed level of normalized mean absolute error.