Chi-square goodness of fit tests for weighted histograms. Review and improvements

TL;DR

This paper reviews chi-square goodness of fit tests for weighted histograms, proposes improvements to enhance their accuracy, and demonstrates their application through numerical examples in simulation contexts.

Contribution

The paper provides a comprehensive review and introduces modifications to chi-square tests for weighted histograms, improving their size accuracy in statistical goodness of fit testing.

Findings

Improved chi-square tests have sizes closer to nominal levels.

Numerical examples demonstrate the effectiveness of the proposed improvements.

Applications in computer simulation contexts are illustrated.

Abstract

Weighted histograms are used for the estimation of probability density functions. Computer simulation is the main domain of application of this type of histogram. A review of chi-square goodness of fit tests for weighted histograms is presented in this paper. Improvements are proposed to these tests that have size more close to its nominal value. Numerical examples are presented in this paper for evaluation of tests and to demonstrate various applications of tests.