whm {rlmDataDriven}

Weighted M-estimation

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 \sqrt(Var) = \sigma = \phi |x^T \beta|^{\gamma} and "exponential" to \sqrt(Var) = \sigma = \phi e^{\gamma |x^T \beta|}.

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)