L2E_TF_dist {L2E}

Solution path of the L2E trend filtering regression with distance penalization

Description

L2E_TF_dist computes the solution path of the robust trend filtering regression under the L2 criterion with distance penalty

Usage

L2E_TF_dist(
  y,
  X,
  beta0,
  tau0,
  D,
  kSeq,
  rhoSeq,
  max_iter = 100,
  tol = 1e-04,
  Show.Time = TRUE
)

Arguments

y

Response vector

X

Design matrix. Default is the identity matrix.

beta0

Initial vector of regression coefficients, can be omitted

tau0

Initial precision estimate, can be omitted

D

The fusion matrix

kSeq

A sequence of tuning parameter k, the number of nonzero entries in D*beta

rhoSeq

An increasing sequence of tuning parameter rho, can be omitted

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 k, the path of estimates for beta (list of matrices) and tau (matrix) for each value of rho, the run time (vector) for each k, and the sequence of rho and k used in the regression (vectors)

Examples

## Completes in 15 seconds

set.seed(12345)
n <- 100
x <- 1:n
f <- matrix(rep(c(-2,5,0,-10), each=n/4), ncol=1)
y <- y0 <- f + rnorm(length(f))

## 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)

D <- myGetDkn(1, n)
k <- c(4,3,2)
rho <- 10^8
# (not run)
# sol <- L2E_TF_dist(y=y, D=D, kSeq=k, rhoSeq=rho)

# 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, sol$Beta[,3], col='blue', lwd=3) ## k=2
# lines(x, sol$Beta[,2], col='red', lwd=3) ## k=3
# lines(x, sol$Beta[,1], col='dark green', lwd=3) ## k=4

## Contaminated Data
ix <- sample(1:n, 10)
y[ix] <- y0[ix] + 2

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

# (not run)
# sol <- L2E_TF_dist(y=y, D=D, kSeq=k, rhoSeq=rho)

# 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, sol$Beta[,3], col='blue', lwd=3) ## k=2
# lines(x, sol$Beta[,2], col='red', lwd=3) ## k=3
# lines(x, sol$Beta[,1], col='dark green', lwd=3) ## k=4