This function obtains the first derivative function of MCP (Minimax Concave Penalty)
dmcp(theta, lambda, gamma = 3)the first derivative of MCP function.
a coefficient vector.
the tuning parameter.
the regularization parameter in MCP (Minimax Concave Penalty). It balances between the unbiasedness and concavity of MCP.
Rigorously speaking, the regularization parametre \(\gamma\) needs to be obtained via a data-driven approach. Published studies suggest experimenting with a few values, such as 1.8, 3, 4.5, 6, and 10, then fixing its value. In our numerical study, we have examined this sequence and found that the results are not sensitive to the choice of value of \(\gamma\), and set the value at 3. In practice, to be prudent, values other than 3 should also be investigated. Similar discussions can be found in the references below.
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 tools:::Rd_expr_doi("10.1002/gepi.22194")
Ren, J., Jung, L., Du, Y., Wu, C., Jiang, Y. and Liu, J. (2019). regnet: Network-Based Regularization for Generalized Linear Models. R package, version 0.4.0
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 tools:::Rd_expr_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 tools:::Rd_expr_doi("10.1186/s12863-017-0495-5")
theta=runif(20,-5,5)
lambda=1
dmcp(theta,lambda,gamma=3)
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