adaHuber.cv.lasso {adaHuber} | R Documentation |
Cross-Validated Regularized Adaptive Huber Regression.
Description
Sparse regularized adaptive Huber regressionwith "lasso" penalty. The function implements a localized majorize-minimize algorithm with a gradient-based method. The regularization parameter \lambda
is selected by cross-validation, and the robustification parameter \tau
is determined by a tuning-free principle.
Usage
adaHuber.cv.lasso(
X,
Y,
lambdaSeq = NULL,
kfolds = 5,
numLambda = 50,
phi0 = 0.01,
gamma = 1.2,
epsilon = 0.001,
iteMax = 500
)
Arguments
X |
A |
Y |
An |
lambdaSeq |
(optional) A sequence of candidate regularization parameters. If unspecified, a reasonable sequence will be generated. |
kfolds |
(optional) Number of folds for cross-validation. Default is 5. |
numLambda |
(optional) Number of |
phi0 |
(optional) The initial quadratic coefficient parameter in the local adaptive majorize-minimize algorithm. Default is 0.01. |
gamma |
(optional) The adaptive search parameter (greater than 1) in the local adaptive majorize-minimize algorithm. Default is 1.2. |
epsilon |
(optional) A tolerance level for the stopping rule. The iteration will stop when the maximum magnitude of the change of coefficient updates is less than |
iteMax |
(optional) Maximum number of iterations. Default is 500. |
Value
An object containing the following items will be returned:
coef
A
(p + 1)
vector of estimated sparse regression coefficients, including the intercept.lambdaSeq
The sequence of candidate regularization parameters.
lambda
Regularization parameter selected by cross-validation.
tau
The robustification parameter calibrated by the tuning-free principle.
iteration
Number of iterations until convergence.
phi
The quadratic coefficient parameter in the local adaptive majorize-minimize algorithm.
References
Pan, X., Sun, Q. and Zhou, W.-X. (2021). Iteratively reweighted l1-penalized robust regression. Electron. J. Stat., 15, 3287-3348.
Sun, Q., Zhou, W.-X. and Fan, J. (2020). Adaptive Huber regression. J. Amer. Statist. Assoc., 115 254-265.
Wang, L., Zheng, C., Zhou, W. and Zhou, W.-X. (2021). A new principle for tuning-free Huber regression. Stat. Sinica, 31, 2153-2177.
See Also
See adaHuber.lasso
for regularized adaptive Huber regression with a specified lambda
.
Examples
n = 100; p = 200; s = 5
beta = c(rep(1.5, s + 1), rep(0, p - s))
X = matrix(rnorm(n * p), n, p)
err = rt(n, 2)
Y = cbind(rep(1, n), X) %*% beta + err
fit.lasso = adaHuber.cv.lasso(X, Y)
beta.lasso = fit.lasso$coef