M_estimation: Psi and Weight Functions for Robust M Estimation

In robts: Robust Time Series Analysis

Description

These psi and corresponding weight functions are employed for robust M estimation and robust filtering.

These functions are intended for internal use and are called for example by the functions acfrob.RA, arrob.filter, filterrob and spectrumrob.pgram.

Usage

M_psi(x, type = c("huber", "bisquare", "smooth"), k)

M_wgt(x, type = c("huber", "bisquare"), k)

smoothpsi(x, k = c(2, 3))

Arguments

x	numeric for which the respective function should be returned. This can either be a single value or a vector.
type	character string giving the type of psi respectively weight function of interest.
k	numeric giving the tuning parameter(s).

Details

The definition of these functions can be accessed by typing M_psi, M_wgt or smoothpsi.

Value

Numeric with the specified psi respectively weight function evaluated at x.

Author(s)

Alexander Dürre, Tobias Liboschik and Jonathan Rathjens

Examples

curve(M_psi(x, type = "huber", k = 2), from = -4, to = 4,
  main = expression(paste("Huber's ", Psi, " function with tuning constant 2")))

curve(M_psi(x, type = "bisquare", k = 3), from = -4, to = 4,
  main = expression(paste("Tukey's ", Psi, " function with tuning constant 3")))

curve(M_psi(x, type = "smooth", k = c(2, 3)), from = -4, to = 4,
  main = expression(paste("Smooth ", Psi, " function with tuning constants 2 and 3")))

robts documentation built on May 2, 2019, 4:55 p.m.