L2E_isotonic {L2E}

L2E isotonic regression

Description

L2E_isotonic performs isotonic regression under the L2 criterion. Available methods include proximal gradient descent (PG) and majorization-minimization (MM).

Usage

L2E_isotonic(
  y,
  beta,
  tau,
  method = "MM",
  max_iter = 100,
  tol = 1e-04,
  Show.Time = TRUE
)

Arguments

y

Response vector

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

set.seed(12345)
n <- 200
tau <- 1
x <- seq(-2.5, 2.5, length.out=n)
f <- x^3
y <- f + (1/tau) * rnorm(n)

## Clean Data
plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)

tau <- 1
b <- y
## Least Squares method
iso <- isotone::gpava(1:n, y)$x
## MM method
sol_mm <- L2E_isotonic(y, b, tau)
## PG method
sol_pg <- L2E_isotonic(y, b, tau, method='PG')

plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)
lines(x, iso, col='blue', lwd=3) ## LS
lines(x, sol_mm$beta, col='red', lwd=3) ## MM
lines(x, sol_pg$beta, col='dark green', lwd=3) ## PG

## Contaminated Data
ix <- 0:9
y[45 + ix] <- 14 + rnorm(10)

plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)

tau <- 1
b <- y
iso <- isotone::gpava(1:n, y)$x
sol_mm <- L2E_isotonic(y, b, tau)
sol_pg <- L2E_isotonic(y, b, tau, method='PG')

plot(x, y, pch=16, cex.lab=1.5, cex.axis=1.5, cex.sub=1.5, col='gray')
lines(x, f, lwd=3)
lines(x, iso, col='blue', lwd=3) ## LS
lines(x, sol_mm$beta, col='red', lwd=3) ## MM
lines(x, sol_pg$beta, col='dark green', lwd=3) ## PG