locpol (version 0.8.0)

thumbBw: Rule of thumb for bandwidth selection.

Description

Implements Fan and Gijbels(1996)'s Rule of thumb for bandwidth selection

Usage

thumbBw(x, y, deg, kernel, weig = rep(1, length(y)))
compDerEst(x, y, p, weig = rep(1, length(y)))

Value

thumbBw returns a single numeric value, while compDerEst returns a data frame whose components are:

x

x values.

y

y values.

res

residuals for the parametric estimation.

der

derivative estimation at x values.

Arguments

x

x covariate data values.

y

y response data values.

p

order of local polynomial estimator.

deg

Local polynomial estimation degree($p$).

kernel

Kernel used to perform the estimation.

weig

weights if they are required.

Author

Jorge Luis Ojeda Cabrera.

Details

See Fan and Gijbels(1996) book, Section 4.2. This implementation is also considering weights. compDerEst computes the \(p+1\) derivative of the regression function in a simple manner, assuming it is a polynomial in \(x\). thumbBw gives a bandwidth selector by means of pilot estimator given by compDerEst and the mean of residuals.

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

regCVBwSelC, pluginBw.

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