FunChisq: Model-Free Functional Chi-Squared and Exact Tests
Yang Zhang, Hua Zhong, Hien Nguyen, Ruby Sharma, Sajal Kumar, Yiyi Li, Mingzhou Joe Song · 2014
Statistical hypothesis testing methods for inferring model-free functional dependency using asymptotic chi-squared or exact distributions. Functional test statistics are asymmetric and functionally optimal, unique from other related statistics. Tests in this package reveal evidence for causality based on the causality-by- functionality principle. They include asymptotic functional chi-squared tests (Zhang & Song 2013) , an adapted functional chi-squared test (Kumar & Song 2022) , and an exact functional test (Zhong & Song 2019) (Nguyen et al. 2020) . The normalized functional chi-squared test was used by Best Performer 'NMSUSongLab' in HPN-DREAM (DREAM8) Breast Cancer Network Inference Challenges (Hill et al. 2016) . A function index (Zhong & Song 2019) (Kumar et al. 2018) derived from the functional test statistic offers a new effect size measure for the strength of functional dependency, a better alternative to conditional entropy in many aspects. For continuous data, these tests offer an advantage over regression analysis when a parametric functional form cannot be assumed; for categorical data, they provide a novel means to assess directional dependency not possible with symmetrical Pearson's chi-squared or Fisher's exact tests.