HCTR - Higher Criticism Tuned Regression

A novel searching scheme for tuning parameter in high-dimensional penalized regression. We propose a new estimate of the regularization parameter based on an estimated lower bound of the proportion of false null hypotheses (Meinshausen and Rice (2006) <doi:10.1214/009053605000000741>). The bound is estimated by applying the empirical null distribution of the higher criticism statistic, a second-level significance testing, which is constructed by dependent p-values from a multi-split regression and aggregation method (Jeng, Zhang and Tzeng (2019) <doi:10.1080/01621459.2018.1518236>). An estimate of tuning parameter in penalized regression is decided corresponding to the lower bound of the proportion of false null hypotheses. Different penalized regression methods are provided in the multi-split algorithm.