est_lambda: Estimate the tuning parameter for a TFRE Lasso regression

In TFRE: A Tuning-Free Robust and Efficient Approach to High-Dimensional Regression

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 <[e-mail]>

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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/01621459.2020.1840989")}.

See Also

TFRE

Examples

n <- 20; p <- 50
X <- matrix(rnorm(n*p),n)
est_lambda(X)

TFRE documentation built on May 29, 2024, 2:19 a.m.