SCAD

0th

Percentile

Penalty function

Smoothly Clipped Absolute Deviation function.

Keywords
models, htest
Usage
SCAD(x, lambda)
Arguments
x

a vector where the function is to be evaluated.

lambda

a number representing a tuning parameter.

Details

SCAD is an even continuous function equal to 0 at x=0, and defined piecewise with derivative lambda in [0, lambda], (a*lambda - x)/(a-1) in [lambda, a*lambda], and 0 for x larger than a*lambda. As suggested by (Li, Sudjianto, 2005), we set a=3.7.

Value

A vector containing the SCAD values at x.

Note

In MLE problems, the penalty value lambda should tend to 0 when the sample size tends to infinity to insure that the asymptotic properties of Penalized-MLE and MLE are the same (see Li, Sudjianto, 2005).

References

R. Li and A. Sudjianto (2005), Analysis of Computer Experiments Using Penalized Likelihood in Gaussian Kriging Models, Technometrics, 47 no. 2, 111-120.

See Also

SCAD.derivative and km for a famous example

Aliases
  • SCAD
Examples
# NOT RUN {
x <- seq(-8,8, length=200)
a <- 3.7

lambda <- 1.5
y <- SCAD(x, lambda)
plot(x, y, type="l", ylim=c(0,6))
x.knots <- c(-a*lambda, -lambda, 0, lambda, a*lambda)
points(x.knots, SCAD(x.knots, lambda), pch=19, cex=0.5)
text(6, SCAD(6, lambda)+0.3, paste("lambda =", lambda))

for (i in 1:2) {
   lambda <- lambda - 0.5
   y <- SCAD(x, lambda)
   lines(x, y, type="l")
   x.knots <- c(-a*lambda, -lambda, 0, lambda, a*lambda)
   points(x.knots, SCAD(x.knots, lambda), pch=19, cex=0.5)
   text(6, SCAD(6, lambda)+0.3, paste("lambda =", lambda))
}

abline(v=0, h=0, lty="dotted")
title("SCAD function")
# }
Documentation reproduced from package DiceKriging, version 1.5.6, License: GPL-2 | GPL-3

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