regCVBwSelC: Cross Validation Bandwidth selector.

In locpol: Kernel Local Polynomial Regression

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)

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.

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.

Value

A numeric value.

Author(s)

Jorge Luis Ojeda Cabrera.

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

locpol documentation built on Nov. 29, 2022, 9:05 a.m.