dmcp {springer}

The first order derivative function of MCP (Minimax Concave Penalty)

Description

The first order derivative function of MCP (Minimax Concave Penalty)

Usage

dmcp(theta, lambda, gamma = 3)

Arguments

theta

a coefficient vector.

lambda

the tuning parameter.

gamma

the regularization parameter for MCP (Minimax Concave Penalty). It balances the unbiasedness and concavity of MCP.

Details

The regularization parameter \gamma for MCP should be obtained via a data-driven approach in a rigorous way. Among the published studies, it is suggested to check several choices, such as 1.4, 3, 4.2, 5.8, 6.9, and 10, then fix the value. We examined this sequence in our study and found that the results are not sensitive to the choice of value for \gamma. Therefore, we set the value to 3. To be prudent, other values should also be examined in practice.

Value

the first order derivative of the MCP function.

References

Ren, J., Du, Y., Li, S., Ma, S., Jiang, Y. and Wu, C. (2019). Robust network-based regularization and variable selection for high-dimensional genomic data in cancer prognosis. Genetic epidemiology, 43(3), 276-291 doi:10.1002/gepi.22194

Wu, C., Zhang, Q., Jiang, Y. and Ma, S. (2018). Robust network-based analysis of the associations between (epi) genetic measurements. Journal of multivariate analysis, 168, 119-130 doi:10.1016/j.jmva.2018.06.009

Ren, J., He, T., Li, Y., Liu, S., Du, Y., Jiang, Y. and Wu, C. (2017). Network-based regularization for high dimensional SNP data in the case-control study of Type 2 diabetes. BMC genetics, 18(1), 44 doi:10.1186/s12863-017-0495-5

Examples

theta=runif(30,-4,4)
lambda=1
dmcp(theta,lambda,gamma=3)