huber: Huber norm and Huber approximations to the ramp and tilted...

In qrnn: Quantile Regression Neural Network

Huber norm and Huber approximations to the ramp and tilted absolute value functions

Description

Huber norm function providing a hybrid L1/L2 norm. Huber approximations to the ramp hramp and tilted absolute value tilted.approx functions. huber.prime, hramp.prime, and tilted.approx.prime provide the corresponding derivatives.

Usage

huber(x, eps)
huber.prime(x, eps)
hramp(x, lower, eps)
hramp.prime(x, lower, eps)
tilted.approx(x, tau, eps)
tilted.approx.prime(x, tau, eps)

Arguments

x	numeric vector.
eps	epsilon value used in huber and related functions.
tau	desired tau-quantile.
lower	left censoring point.

See Also

tilted.abs, qrnn.cost

Examples

x <- seq(-10, 10, length=100)
plot(x, huber(x, eps=1), type="l", col="black", ylim=c(-2, 10), ylab="")
lines(x, hramp(x, lower=0, eps=1), col="red")
lines(x, tilted.approx(x, tau=0.1, eps=1), col="blue")
lines(x, huber.prime(x, eps=1), col="black", lty=2)
lines(x, hramp.prime(x, lower=0, eps=1), lty=2, col="red")
lines(x, tilted.approx.prime(x, tau=0.1, eps=1), lty=2, col="blue")

qrnn documentation built on May 29, 2024, 1:27 a.m.