rlmDataDriven (version 0.4.0)

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

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

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

# NOT RUN {
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)


# }