L2E isotonic regression

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

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)

#>    user  system elapsed 
#>   0.042   0.000   0.041 
## PG method
sol_pg <- L2E_isotonic(y, b, tau, method='PG')

#>    user  system elapsed 
#>   0.221   0.000   0.221 

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)

#>    user  system elapsed 
#>   0.043   0.000   0.044 
sol_pg <- L2E_isotonic(y, b, tau, method='PG')

#>    user  system elapsed 
#>   0.125   0.000   0.125 

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