robustSmoothSpline: Robust fit of a Smoothing Spline

In HenrikBengtsson/aroma.light: Light-Weight Methods for Normalization and Visualization of Microarray Data using Only Basic R Data Types

Robust fit of a Smoothing Spline

Description

Fits a smoothing spline robustly using the L_1 norm. Currently, the algorithm is an iterative reweighted smooth spline algorithm which calls smooth.spline(x,y,w,...) at each iteration with the weights w equal to the inverse of the absolute value of the residuals for the last iteration step.

Usage

## Default S3 method:
robustSmoothSpline(x, y=NULL, w=NULL, ..., minIter=3, maxIter=max(minIter, 50),
  method=c("L1", "symmetric"), sdCriteria=2e-04, reps=1e-15, tol=1e-06 * IQR(x),
  plotCurves=FALSE)

Arguments

x	a vector giving the values of the predictor variable, or a list or a two-column matrix specifying x and y. If x is of class smooth.spline then x$x is used as the x values and x$yin are used as the y values.
y	responses. If y is missing, the responses are assumed to be specified by x.
w	a vector of weights the same length as x giving the weights to use for each element of x. Default value is equal weight to all values.
...	Other arguments passed to smooth.spline.
minIter	the minimum number of iterations used to fit the smoothing spline robustly. Default value is 3.
maxIter	the maximum number of iterations used to fit the smoothing spline robustly. Default value is 25.
method	the method used to compute robustness weights at each iteration. Default value is "L1", which uses the inverse of the absolute value of the residuals. Using "symmetric" will use Tukey's biweight with cut-off equal to six times the MAD of the residuals, equivalent to lowess.
sdCriteria	Convergence criteria, which the difference between the standard deviation of the residuals between two consecutive iteration steps. Default value is 2e-4.
reps	Small positive number added to residuals to avoid division by zero when calculating new weights for next iteration.
tol	Passed to smooth.spline (R >= 2.14.0).
plotCurves	If TRUE, the fitted splines are added to the current plot, otherwise not.

Value

Returns an object of class smooth.spline.

Author(s)

Henrik Bengtsson

See Also

This implementation of this function was adopted from smooth.spline of the stats package. Because of this, this function is also licensed under GPL v2.

Examples

data(cars)
attach(cars)
plot(speed, dist, main = "data(cars)  &  robust smoothing splines")

# Fit a smoothing spline using L_2 norm
cars.spl <- smooth.spline(speed, dist)
lines(cars.spl, col = "blue")

# Fit a smoothing spline using L_1 norm
cars.rspl <- robustSmoothSpline(speed, dist)
lines(cars.rspl, col = "red")

# Fit a smoothing spline using L_2 norm with 10 degrees of freedom
lines(smooth.spline(speed, dist, df=10), lty=2, col = "blue")

# Fit a smoothing spline using L_1 norm with 10 degrees of freedom
lines(robustSmoothSpline(speed, dist, df=10), lty=2, col = "red")

legend(5,120, c(
    paste("smooth.spline [C.V.] => df =",round(cars.spl$df,1)),
    paste("robustSmoothSpline [C.V.] => df =",round(cars.rspl$df,1)),
    "standard with s( * , df = 10)", "robust with s( * , df = 10)"
  ), col = c("blue","red","blue","red"), lty = c(1,1,2,2), bg='bisque')

HenrikBengtsson/aroma.light documentation built on July 3, 2023, 1:57 a.m.