locpol (version 0.8.0)

pluginBw: Plugin Bandwidth selector.

Description

Implements a plugin bandwidth selector for the regression function.

Usage

pluginBw(x, y, deg, kernel, weig = rep(1,length(y)))

Value

A numeric value.

Arguments

x

x covariate values.

y

y response values.

deg

degree of the local polynomial.

kernel

Kernel used to perform the estimation, see Kernels.

weig

Vector of weights for observations.

Author

Jorge Luis Ojeda Cabrera.

Details

Computes the plug-in bandwidth selector as shown in Fan and Gijbels(1996) book using pilots estimates as given in page 110-112 (Rule of thumb for bandwidth selection). Currently, only even values of p are can be used.

References

Fan, J. and Gijbels, I. Local polynomial modelling and its applications\/. Chapman & Hall, London (1996).

Wand, M.~P. and Jones, M.~C. Kernel smoothing\/. Chapman and Hall Ltd., London (1995).

See Also

thumbBw, regCVBwSelC.

Examples

	size <- 200
	sigma <- 0.25
	deg <- 1
	kernel <- EpaK
	xeval <- 0:100/100
	regFun <- function(x) x^3
	x <- runif(size)
	y <- regFun(x) + rnorm(x, sd = sigma)
	d <- data.frame(x, y)
	cvBwSel <- regCVBwSelC(d$x,d$y, deg, kernel, interval = c(0, 0.25))
	thBwSel <- thumbBw(d$x, d$y, deg, kernel)
	piBwSel <- pluginBw(d$x, d$y, deg, kernel)
	est <- function(bw, dat, x) return(locPolSmootherC(dat$x,dat$y, x, bw, deg,
					kernel)$beta0)
	ise <- function(val, est) return(sum((val - est)^2 * xeval[[2]]))
	plot(d$x, d$y)
	trueVal <- regFun(xeval)
	lines(xeval, trueVal, col = "red")
	xevalRes <- est(cvBwSel, d, xeval)
	cvIse <- ise(trueVal, xevalRes)
	lines(xeval, xevalRes, col = "blue")
	xevalRes <- est(thBwSel, d, xeval)
	thIse <- ise(trueVal, xevalRes)
	xevalRes <- est(piBwSel, d, xeval)
	piIse <- ise(trueVal, xevalRes)
	lines(xeval, xevalRes, col = "blue", lty = "dashed")
	res <- rbind(	bw = c(cvBwSel, thBwSel, piBwSel),
					ise = c(cvIse, thIse, piIse) )
	colnames(res) <- c("CV", "th", "PI")
	res