rlmDD {rlmDataDriven}

Data driven robust methods

Description

Robust estimation often relies on a dispersion function that is more slowly varying at large values than the squared function. However, the choice of tuning constant in dispersion function may impact the estimation efficiency to a great extent. For a given family of dispersion functions, we suggest obtaining the ‘best’ tuning constant from the data so that the asymptotic efficiency is maximized.

This library provides a robust linear regression with a tuning parameter being automatically chosen to provide the necessary resistance against outliers. The robust (loss) functions include the Huber, Tukey bisquare and the exponential loss.

Usage

rlmDD(yy, xx, beta0, betaR, method, plot)

Arguments

yy

Vector representing the response variable

xx

Design matrix of the covariates excluding the intercept in the first column

beta0

Initial parameter estimate using lm

betaR

Robust estimate of beta with a fixed tuning constant using rlm

method

Huber, Bisquare or Exponential

plot

"Y" gives a plot: the efficiency factor versus a range of tunning parameter values.

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)

You-Gan Wang, Na Wang

References

Wang, Y-G., Lin, X., Zhu, M., & Bai, Z. (2007). Robust estimation using the Huber function with a data-dependent tuning constant. Journal of Computational and Graphical Statistics, 16(2), 468-481.

Wang, X., Jiang, Y., Huang, M., & Zhang, H. (2013). Robust variable selection with exponential squared loss. Journal of the American Statistical Association, 108, 632-643.

Wang, N., Wang, Y-G., Hu, S., Hu, Z. H., Xu, J., Tang, H., & Jin, G. (2018). Robust Regression with Data-Dependent Regularization Parameters and Autoregressive Temporal Correlations. Environmental Modeling & Assessment, in press.

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)
DD1 <- rlmDD(stack.loss, stack.x, LS$coef, RB$coef, method = "Huber", 
plot = "Y")

LS <- lm(stack.loss ~ stack.x)
RB <- rlm(stack.loss ~ stack.x, psi = psi.bisquare, c = 4.685)
DD2 <- rlmDD(stack.loss, stack.x, LS$coef, RB$coef, method = "Bisquare", 
plot = "Y")

LS <- lm(stack.loss ~ stack.x)
RB <- rlm(stack.loss ~ stack.x, psi = psi.huber, k = 1.345)
DD3 <- rlmDD(stack.loss, stack.x, LS$coef, RB$coef, method = "Exponential",
plot = "Y")


## Plasma dataset


data(plasma)

y <- plasma$y
x <- cbind(plasma$calories, plasma$dietary)

LS <- lm(y ~ x)
RB <- rlm(y ~ x, psi = psi.huber, k = 1.345)
DD.h <- rlmDD(y, x, LS$coef, RB$coef, method = "Huber", plot = "Y")

LS <- lm(y ~ x)
RB <- rlm(y ~ x, psi = psi.bisquare, c = 4.685)
DD.b <- rlmDD(y, x, LS$coef, RB$coef, method = "Bisquare", plot = "Y")

LS <- lm(y ~ x)
RB <- rlm(y ~ x, psi = psi.huber, k = 1.345)
DD.e <- rlmDD(y, x, LS$coef, RB$coef, method = "Exponential", plot = "Y")