Description
Higher Criticism Tuned Regression.
Description
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.
README.md
HCTR
The goal of HCTR is to create a new searching scheme for the regularization parameter in penalized regression, such as Lasso, adaptive Lasso, SCAD, and MCP.
Example
This is a basic example which shows you how to (1) estimate false null hypothesis proportion, and (2) create a new tuning region for the regularization parameter.
## basic example code
library('HCTR')
# 1. Estimate proportion
set.seed(10)
X <- matrix(runif(n = 10000, min = 0, max = 1), nrow = 100)
result <- bounding.seq(p.value = X)
Y <- matrix(runif(n = 100, min = 0, max = 1), nrow = 100)
test <- est.prop(p.value = Y, cn = result)
# 2. Estimate a new tuning region
set.seed(10)
X <- matrix(rnorm(20000), nrow = 100)
beta <- rep(0, 200)
beta[1:100] <- 5
Y <- MASS::mvrnorm(n = 1, mu = X%*%beta, Sigma = diag(100))
fit <- glmnet::cv.glmnet(x = X, y = Y)
pihat <- 0.01
result <- est.lambda(cv.fit = fit, pihat = pihat, p = ncol(X))