L2E_sparse_ncv {L2E}

Solution path of L2E sparse regression with existing penalization methods

Description

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

Usage

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")
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")
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)