On statistical methods of structure function extraction

TL;DR

This paper compares various statistical methods, including orthogonal weight functions and chi-squared minimization, for extracting structure functions from deep inelastic scattering data, analyzing their effectiveness through bias and variance metrics.

Contribution

It introduces and evaluates new statistical approaches for structure function extraction, providing a comparative analysis of their performance.

Findings

Orthogonal weight function method reduces bias.

Chi-squared minimization is effective for error minimization.

Different methods show varying variance and bias levels.

Abstract

Several methods of statistical analysis are proposed and analyzed in application for a specific task -- extraction of the structure functions from the cross sections of deep inelastic interactions of any type. We formulate the method based on the orthogonal weight functions and on an optimization procedure of errors minimization as well as methods underlying common $\chi^2$ minimization. Effectiveness of these methods usage is analyzed by comparison of the statistical parameters such as bias, extraction variance etc., for sample deep inelastic scattering data set.