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.
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