robust sparse regression under cellwise contamination with a grid of lambdas (standardize predictors first)

Usage

sregcell_std(
  y,
  x,
  scale.method = qnscale,
  df = Inf,
  softbeta = TRUE,
  softdelta = TRUE,
  softzeta = TRUE,
  lambda_delta = NULL,
  lambda_zeta = 1,
  prob = 0.995,
  alpha = 0.5,
  penal = 1,
  penaldelta = 0,
  tol = 0.001,
  maxiter = 30
)

Arguments

y: n-dimensional response vector
x: nxp design matrix
scale.method: method we used to obtain robust scales, by default is qn
df: degrees of freedom of the assuming distribution of predictors
softbeta: whether to use soft/hard threshold for beta
softdelta: whether to use soft/hard threshold for delta(outliers in x)
softzeta: whether to use soft/hard threshold for zeta(outliers in y)
lambda_delta: tuning parameter of delta
lambda_zeta: tuning parameter of zeta
prob: probability of quantiles, by default is 0.995
alpha: the importance factor of the regression loss (between 0-1, by default is 0.5)
penal: the penalty parameter for model selection (by default is 1, equivalent to BIC )
penaldelta: the penalty of number of detected outliers (for further development, by default is 0)
tol: the tolerance of convergence, by default is 1e-3
maxiter: number of iterations, by default is 100

Value

betahat: the estimated beta

intercept_hat: the estimated intercept

betahat_opt: the estimated beta with post-cellwise-robust regression

intercept_opt: the estimated intercept with post-cellwise-robust regression

...

Examples

data = genevar()
y = data$y
x = data$x
fit = sregcell_std(y,x)