02: Boosting C-statistics in Astronomy: Higher-order Asymptotics for Improved Goodness-of-fit Testing

Music City Center 

In astrophysics, the C statistic, which is a likelihood ratio statistic, has been
widely adopted for model fitting and goodness-of-fit assessments for Poisson-count
data with heterogeneous rates. In many astronomy and high-energy physics applications, the observations are sparse, making the theoretical properties of C-statistics questionable. Over the past decade, researchers have gradually realized the problems of directly applying the C-statistics for such small count data and published approximate solutions. In this paper, we comprehensively study the properties of C-statistics and evaluate various algorithms for goodness-of-fit assessment using C-statistics, emphasizing lowcount scenarios. Theoretical results, computational algorithms, extensive simulation
studies, and real data applications will be presented. We show both theoretically and numerically that (a) classical χ2-based goodness-of-fit assessment is not effective in low-count settings, (b) vanilla bootstrap with moment estimators of the mean and variances result in biases in estimated null distribution and (c)
high-order asymptotic achieves good precision, with a much lower computation cost.

Goodness-of-fit

Low Count Data

C-statisitics

Bootstrap

High-energy Physics 

Astrostatistics Interest Group