| est_lambda {TFRE} | R Documentation |
Estimate the tuning parameter for a TFRE Lasso regression
Description
Estimate the tuning parameter of the TFRE Lasso regression given the covariate matrix X.
Usage
est_lambda(X, alpha0 = 0.1, const_lambda = 1.01, times = 500)
Arguments
X |
Input matrix, of dimension n_obs x n_vars; each row is an observation vector. |
alpha0 |
The level to estimate the tuning parameter. Default value is 0.1. See more details in "Details". |
const_lambda |
The constant to estimate the tuning parameter, should be greater than 1. Default value is 1.01. See more details in "Details". |
times |
The size of simulated samples to estimate the tuning parameter. Default value is 500. |
Details
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.
Value
The estimated tuning parameter of the TFRE Lasso regression given X.
Author(s)
Yunan Wu and Lan Wang
Maintainer:
Yunan Wu <yunan.wu@utdallas.edu>
References
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, doi:10.1080/01621459.2020.1840989.
See Also
Examples
n <- 20; p <- 50
X <- matrix(rnorm(n*p),n)
est_lambda(X)