span.H.select: A method to select the span of the sequence of lambda's for...

In NPsimex: Nonparametric Smoothing for contaminated data using Simulation-Extrapolation

Description

To compute the optimal span of the sequence of lambda's for the case of heteroscedastic error.

Usage

 span.H.select(W, msigma, span=c(2,4,6,8,10,12,25), approx=FALSE, from=min(W), to=max(W), n.user=128, n.lambda=50, lambda="SJ", bw="SJ", adjust=1, na.rm = FALSE, ...)

Arguments

W	The observed data. It is a vector of length at least 10.
msigma	The standard deviation σ of measurement error. It is a single positive numeric value.
span	span is user-defined grids where the PDF will be evaluated.
approx	FALSE by default; if TRUE, the lose function uses the same one as the one of the homoscedastic error case with the average of measurement error variances
from	the starting point where the PDF is to be evaluated.
to	the starting point where the PDF is to be evaluated.
n.user	number of points where the PDF is to be evaluated.
n.lambda	number of points of lambda's.
lambda	Specifies the first lambda. It can be a single numeric value which has been pre-determined; or computed with the specific density bandwidth selector: 'nrd0', 'nrd', 'ucv', 'bcv', 'SJ'.
bw	Specifies the bandwidth of 'W'. It can be a single numeric value which has been pre-determined; or computed with the specific density bandwidth selector: 'nrd0', 'nrd', 'ucv', 'bcv', 'SJ'.
adjust	adjust the range there the PDF is to be evaluated. By default, adjust=1.
na.rm	is set to FALSE by default: no NA value is allowed.
...	control

Author(s)

X.F. Wang [e-mail]

References

Wang, X.F., Sun, J. and Fan, Z. (2011). Deconvolution density estimation with heteroscedastic errors using SIMEX.

See Also

simex.density.

Examples

plot.simex.density <- function(X.simex,X,...){
	plot(X.simex$x, X.simex$y, type="l", xlab="x", ylab="density", lwd=3, lty=2, col=2,...)
	lines(density(X, bw="SJ"), lwd=3)
	}

############### Heteroscadestic error
N <- 1000
set.seed(123); X <- c(rnorm(N/2, mean=-2), rnorm(N/2,mean=2)); U <- rnorm(N,sd=1); msigma <- runif(N,min=0.3,max=0.5)
W <- X + msigma*U

plot.simex.density <- function(X.simex,X,...){
	plot(X.simex$x, X.simex$y, type="l", xlab="x", ylab="density", lwd=3, lty=2, col=2,...)
	lines(density(X, bw="SJ"), lwd=3)
	}


#---- Select the optimal lambda span
par(mfrow=c(1,2))
spans <- span.H.select(W, msigma, span=c(2,4,6,8,10,12,16,25), approx=TRUE)
plot(spans$span, spans$ISE, type="o", xlab="span", ylab="ISE") 

X.simex <- simex.H.density(W, msigma=msigma, adjust=1, n.lambda=50, span=spans$span[order(spans$ISE)[1]])
plot.simex.density(X.simex, X,ylim=c(0,0.25))

## more computational time needed if approx=FALSE.

# spans <- span.H.select(W, msigma, span=c(2,4,6,8,10,12,16,25), approx=FALSE)
# plot(spans$span, spans$ISE, type="o", xlab="span", ylab="ISE") 
# 
# X.simex <- simex.H.density(W, msigma=msigma, adjust=1, n.lambda=50, span=spans$span[order(spans$ISE)[1]])
# plot.simex.density(X.simex, X,ylim=c(0,0.25))

NPsimex documentation built on May 1, 2019, 6:32 p.m.