whm: Weighted M-estimation

In rlmDataDriven: Robust Regression with Data Driven Tuning Parameter

Description

This function performs a weighted M-estimation described by Carroll and Ruppert (1982) with the Huber loss function. First, a M-estimation is performed on the data assuming that the variance is constant. The residuals of this model are used to robustly estimate the variance parameter. Then, a weighted M-estimation with variance as weight is used to update the regression parameters. These steps are iterated until desired convergence.

Usage

whm(yy, xx, var.function = "power", tuning.para = 1.345, ite = 5)

Arguments

yy	Vector representing the response variable
xx	Design matrix of the covariates including the intercept in the first column
var.function	Assumed function for the variance. "power" function corresponds to √(Var) = σ = φ |x^T β|^{γ} and "exponential" to √(Var) = σ = φ e^{γ |x^T β|}.
tuning.para	Value of the tuning parameter associated with the loss function.
ite	Number of iterations for the estimation procedure.

Value

The function returns a list including

esti	Value of the robust estimate
Std.Error	Standard error of the robust estimate
tunning	Optimum tunning parameter
R2	R-squared value

Author(s)

Aurelien Callens, You-Gan Wang, Benoit Liquet.

References

Carroll, R. J., & Ruppert, D. (1982). Robust estimation in heteroscedastic linear models. The annals of statistics, 429-441.

See Also

rlm function from package MASS

Examples

library(MASS)
data(stackloss)

LS <- lm(stack.loss ~ stack.x)
RB <- rlm(stack.loss ~ stack.x, psi = psi.huber, k = 1.345)

yy <- stack.loss 
xx <- model.matrix(stack.loss ~ stack.x)

#With power function as variance function
WHM_p <- whm(yy, xx, var.function = "power", tuning.para = 1.345)

#With exponential function as variance function
WHM_e <- whm(yy, xx, var.function = "exponential", tuning.para = 1.345)

rlmDataDriven documentation built on Oct. 3, 2019, 5:04 p.m.