LLsharpen {sharpData}

Data Sharpening for Local Linear Regression

Description

Calculation of sharpened responses for bias reduction in function and first derivative estimation, assuming a gaussian kernel is used in bivariate scatterplot smoothing.

Usage

LLsharpen(x, y, h)

Arguments

x

a numeric vector containing the predictor variable values.

y

a numeric vector containing the response variable values.

h

a numeric vector containing the (scalar) bandwidth.

Value

a vector containing the sharpened (i.e. perturbed) response values, ready for input into a local linear regression estimator.

Author(s)

W.J. Braun

References

Choi, E., Hall, P. and Rousson, V. (2000) Data sharpening methods for bias reduction in nonparametric regression. Annals of Statistics 28(5) 1339-1355.

See Also

locpoly

Examples

speed <- MPG[, 1]
mpg <- MPG[, 2]
h <- dpill(speed, mpg)*2
mpgSharp <- LLsharpen(speed, mpg, h)
mpg.lS <- locpoly(speed, mpgSharp, bandwidth=h, drv=1, degree=1)
mpg.lX <- locpoly(speed, mpg, bandwidth=h, drv=1, degree=1)
plot(mpg.lX, type="l")  # unsharpened derivative estimation
lines(mpg.lS, col=2, lty=2)  # sharpened derivative estimation