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

Usage

sregcell(
  y,
  x,
  betahat = NULL,
  intercept = NULL,
  softbeta = TRUE,
  softdelta = TRUE,
  softzeta = TRUE,
  lambda_delta = 2.56,
  lambda_zeta = 2.56,
  alpha = 0.5,
  penal = 1,
  penaldelta = 1,
  tol = 0.001,
  maxiter = 100
)

Arguments

y: n-dimensional response vector
x: nxp design matrix
betahat: p-dimensional initial estimate of beta
intercept: initial estimate of intercept
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
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 estiamted intercept

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

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

allfits: a list of results including all outputs from all candidate tuning parameters

...

Examples


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