L2E_multivariate {L2E}

L2E multivariate regression

Description

L2E_multivariate performs multivariate regression under the L2 criterion. Available methods include proximal gradient descent (PG) and majorization-minimization (MM).

Usage

L2E_multivariate(
  y,
  X,
  beta,
  tau,
  method = "MM",
  max_iter = 100,
  tol = 1e-04,
  Show.Time = TRUE
)

Arguments

y

Response vector

X

Design matrix

beta

Initial vector of regression coefficients

tau

Initial precision estimate

method

Available methods include PG and MM. MM by default.

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 (vector) and tau (scalar), the number of outer block descent iterations until convergence (scalar), and the number of inner iterations per outer iteration for updating beta (vector) and tau or eta (vector)

Examples

# Bank data example
y <- bank$y
X <- as.matrix(bank[,1:13])
X0 <- as.matrix(cbind(rep(1,length(y)), X))

tau <- 1/mad(y)
b <- matrix(0, 14, 1)

# MM method
sol_mm <- L2E_multivariate(y, X0, b, tau)
r_mm <- y - X0 %*% sol_mm$beta
ix_mm <- which(abs(r_mm) > 3/sol_mm$tau)
l2e_fit_mm <- X0 %*% sol_mm$beta

# PG method
sol_pg <- L2E_multivariate(y, X0, b, tau, method="PG")
r_pg <- y - X0 %*% sol_pg$beta
ix_pg <- which(abs(r_pg) > 3/sol_pg$tau)
l2e_fit_pg <- X0 %*% sol_pg$beta

plot(y, l2e_fit_mm, ylab='Predicted values', main='MM', pch=16, cex=0.8) # MM
points(y[ix_mm], l2e_fit_mm[ix_mm], pch=16, col='blue', cex=0.8) # MM
plot(y, l2e_fit_pg, ylab='Predicted values', main='PG', pch=16, cex=0.8) # PG
points(y[ix_pg], l2e_fit_pg[ix_pg], pch=16, col='blue', cex=0.8) # PG