gcmlcm {fdrtool} R Documentation

## Greatest Convex Minorant and Least Concave Majorant

### Description

`gcmlcm` computes the greatest convex minorant (GCM) or the least concave majorant (LCM) of a piece-wise linear function.

### Usage

```gcmlcm(x, y, type=c("gcm", "lcm"))
```

### Arguments

 `x, y` coordinate vectors of the piece-wise linear function. Note that the x values need to be unique and be arranged in sorted order. `type` specifies whether to compute the greatest convex minorant (`type="gcm"`, the default) or the least concave majorant (`type="lcm"`).

### Details

The GCM is obtained by isotonic regression of the raw slopes, whereas the LCM is obtained by antitonic regression. See Robertson et al. (1988).

### Value

A list with the following entries:

 `x.knots` the x values belonging to the knots of the LCM/GCM curve `y.knots` the corresponding y values `slope.knots` the slopes of the corresponding line segments

### Author(s)

Korbinian Strimmer (https://strimmerlab.github.io).

### References

Robertson, T., F. T. Wright, and R. L. Dykstra. 1988. Order restricted statistical inference. John Wiley and Sons.

`monoreg`.

### Examples

```# load "fdrtool" library
library("fdrtool")

# generate some data
x = 1:20
y = rexp(20)
plot(x, y, type="l", lty=3, main="GCM (red) and LCM (blue)")
points(x, y)

# greatest convex minorant (red)
gg = gcmlcm(x,y)
lines(gg\$x.knots, gg\$y.knots, col=2, lwd=2)

# least concave majorant (blue)
ll = gcmlcm(x,y, type="lcm")
lines(ll\$x.knots, ll\$y.knots, col=4, lwd=2)

```

[Package fdrtool version 1.2.17 Index]