Comparison of methods to extract an asymmetry parameter from data

TL;DR

This paper compares various statistical methods for extracting an asymmetry parameter from data, introducing an improved weighting technique that matches the likelihood method's precision across all asymmetry levels.

Contribution

It presents an enhanced weighting procedure that achieves the same statistical efficiency as the maximum likelihood method for any asymmetry value.

Findings

Improved weighting method reaches the likelihood method's FOM for all asymmetries.

Comparison shows the methods' applicability and precision differences.

Maximum likelihood method's limitations are discussed.

Abstract

Several methods to extract an asymmetry parameter in an event distribution function are discussed and compared in terms of statistical precision and applicability. These methods are: simple counting rate asymmetries, event weighting procedures and the unbinned extended maximum likelihood method. It is known that weighting methods reach the same figure of merit (FOM) as the likelihood method in the limit of vanishing asymmetries. This article presents an improved weighting procedure reaching the FOM of the likelihood method for arbitrary asymmetries. Cases where the maximum likelihood method is not applicable are also discussed.