Soft-thresholded ridge (STR) estimator

Fits the soft-thresholded ridge estimator \(\hat\theta_j = sign(\hat\beta_{k,j})(|\hat\beta_{k,j}| - \gamma)_+\), where \(\hat\beta_k\) is the ridge estimator with ridge parameter k. The estimator has an explicit form and is valid for \(p > n\).

Usage

hr(
  X,
  y,
  k,
  gamma,
  intercept = TRUE,
  standardize = TRUE,
  nonneg = FALSE,
  scale = FALSE
)

# S3 method for class 'hr'
coef(object, ik = 1, ig = 1, ...)

# S3 method for class 'hr'
predict(object, newx, ik = 1, ig = 1, ...)

Arguments

X: n x p design matrix.
y: response vector of length n.
k: ridge parameter(s), positive.
gamma: threshold(s), nonnegative. Thresholds apply on the scale of the standardized design when standardize = TRUE.
intercept: logical, fit an unpenalized intercept by centring.
standardize: logical, scale columns of X to unit variance.
nonneg: logical, use the nonnegative variant \((\hat\beta_{k,j} - \gamma)_+\).
scale: For hr, logical training least-squares rescaling (SSTR-LS). For hr_risk, a fixed positive numeric scale; not a random fitted scale.
object: a fitted "hr" object.
ik, ig: indices of the ridge parameter and threshold to use.
...: unused.
newx: matrix of new predictor values.

Value

An object of class "hr" containing the coefficient array beta of dimension p x length(k) x length(gamma) on the original scale, the intercepts a0, and the tuning grids.

Examples

set.seed(1)
X <- matrix(rnorm(50 * 200), 50, 200)
y <- X[, 1:3] %*% c(3, -2, 1.5) + rnorm(50)
fit <- hr(X, y, k = 10, gamma = 0.1)
which(coef(fit)[-1] != 0)
#>  [1]   1   2   3  10  11  18  19  22  25  26  27  28  37  39  44  47  49  52  55
#> [20]  60  65  66  68  73  78  81  88  90  92  96  97  98 100 101 102 105 113 115
#> [39] 119 121 122 126 128 130 132 134 136 138 140 144 148 149 151 162 163 164 165
#> [58] 167 172 174 175 176 181 182 185 191 192 193 197 199 200