Goodness of fit tests for weighted histograms

TL;DR

This paper develops and evaluates goodness of fit tests specifically designed for weighted histograms used in Monte Carlo simulations, addressing the challenges posed by weights and unknown normalization.

Contribution

It introduces new goodness of fit tests tailored for weighted histograms, including those with unknown normalization, and assesses their performance through numerical studies.

Findings

Tests have appropriate size and power in simulations

Proposed methods effectively handle weights in histograms

New tests outperform some existing approaches

Abstract

Weighted histogram in Monte-Carlo simulations is often used for the estimation of a probability density function. It is obtained as a result of random experiment with random events that have weights. In this paper the bin contents of weighted histogram are considered as a sum of random variables with random number of terms. Goodness of fit tests for weighted histograms and for weighted histograms with unknown normalization are proposed. Sizes and powers of the tests are investigated numerically.