DiceKriging (version 1.6.0)

# SCAD: Penalty function

## Description

Smoothly Clipped Absolute Deviation function.

## Usage

`SCAD(x, lambda)`

## Arguments

x

a vector where the function is to be evaluated.

lambda

a number representing a tuning parameter.

## Value

A vector containing the SCAD values at `x`.

## 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`.

## 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

## 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")
# }
```