Solution path of L2E sparse regression with existing penalization methods

L2E_sparse_ncv computes the solution path of robust sparse regression under the L2 criterion. Available penalties include lasso, MCP and SCAD.

L2E_sparse_ncv(
  y,
  X,
  b,
  tau,
  lambdaSeq,
  penalty = "MCP",
  max_iter = 100,
  tol = 1e-04,
  Show.Time = TRUE
)

Arguments

y	Response vector
X	Design matrix
b	Initial vector of regression coefficients, can be omitted
tau	Initial precision estimate, can be omitted
lambdaSeq	A decreasing sequence of values for the tuning parameter lambda, can be omitted
penalty	Available penalties include lasso, MCP and SCAD.
max_iter	Maximum number of iterations
tol	Relative tolerance
Show.Time	Report the computing time

Value

Returns a list object containing the estimates for beta (matrix) and tau (vector) for each value of the tuning parameter lambda, the run time (vector) for each lambda, and the sequence of lambda used in the regression (vector)

Examples

set.seed(12345)
n <- 100
tau <- 1
f <- matrix(c(rep(2,5), rep(0,45)), ncol = 1)
X <- X0 <- matrix(rnorm(n*50), nrow = n)
y <- y0 <- X0 %*% f + (1/tau)*rnorm(n)

## Clean Data
lambda <- 10^(-1)
sol <- L2E_sparse_ncv(y=y, X=X, lambdaSeq=lambda, penalty="SCAD")
#>    user  system elapsed 
#>   0.015   0.000   0.015 
r <- y - X %*% sol$Beta
ix <- which(abs(r) > 3/sol$Tau)
l2e_fit <- X %*% sol$Beta

plot(y, l2e_fit, ylab='Predicted values', pch=16, cex=0.8)
points(y[ix], l2e_fit[ix], pch=16, col='blue', cex=0.8)

## Contaminated Data
i <- 1:5
y[i] <- 2 + y0[i]
X[i,] <- 2 + X0[i,]

sol <- L2E_sparse_ncv(y=y, X=X, lambdaSeq=lambda, penalty="SCAD")
#>    user  system elapsed 
#>   0.048   0.000   0.048 
r <- y - X %*% sol$Beta
ix <- which(abs(r) > 3/sol$Tau)
l2e_fit <- X %*% sol$Beta

plot(y, l2e_fit, ylab='Predicted values', pch=16, cex=0.8)
points(y[ix], l2e_fit[ix], pch=16, col='blue', cex=0.8)