Estimate the tuning parameter of the TFRE Lasso regression given the covariate matrix X.
est_lambda(X, alpha0 = 0.1, const_lambda = 1.01, times = 500)The estimated tuning parameter of the TFRE Lasso regression given X.
Input matrix, of dimension n_obs x n_vars; each row is an observation vector.
The level to estimate the tuning parameter. Default value is 0.1. See more details in "Details".
The constant to estimate the tuning parameter, should be greater than 1. Default value is 1.01. See more details in "Details".
The size of simulated samples to estimate the tuning parameter. Default value is 500.
Yunan Wu and Lan Wang
Maintainer:
Yunan Wu <yunan.wu@utdallas.edu>
In TFRE Lasso regressions, the tuning parameter can be estimated independent of errors. In Wang et al. (2020), the following tuning parameter is suggested: $$\lambda^* = const\_lambda * G^{-1}_{||\bm{S}_n||_\infty}(1-alpha0)$$, where \(\bm{S}_n = -2[n(n-1)]^{-1}\sum_{j=1}^n\bm{x}_j[2r_j-(n+1)]\), \(r_1,\ldots,r_n\) follows the uniform distribution on the per-mutations of the integers \(\{1,\ldots,n\}\), and \(G^{-1}_{||\bm{S}_n||_\infty}(1-alpha0)\) denotes the \((1-alpha0)\)-quantile of the distribution of \(||\bm{S}_n||_\infty\).
Wang, L., Peng, B., Bradic, J., Li, R. and Wu, Y. (2020), A Tuning-free Robust and Efficient Approach to High-dimensional Regression, Journal of the American Statistical Association, 115:532, 1700-1714, tools:::Rd_expr_doi("10.1080/01621459.2020.1840989").
TFRE
n <- 20; p <- 50
X <- matrix(rnorm(n*p),n)
est_lambda(X)
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