locpol (version 0.8.0)

regCVBwSelC: Cross Validation Bandwidth selector.

Description

Implements Cross validation bandwidth selector for the regression function.

Usage

regCVBwSelC(x, y, deg, kernel=gaussK,weig=rep(1,length(y)),
interval=.lokestOptInt)

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.

interval

An interval where to look for the bandwidth.

Author

Jorge Luis Ojeda Cabrera.

Details

Computes the weighted ASE for every bandwidth returning the minimum. The function is implemented by means of a C function that computes for a single bandwidth the ASE, and a call to optimise on a given interval.

References

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

H\"ardle W.(1990) Smoothing techniques. Springer Series in Statistics, New York (1991).

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

See Also

thumbBw, 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