Perform nonparametric regression with errors-in-variables

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Description

To perform nonparametric regression with errors-in-variables. The measurement errors can be either homoscedastic or heteroscedastic.

Usage

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DeconNpr(y,sig,z,x,error='normal',bw='dboot1',adjust=1,
	n=512,from,to,cut=3,na.rm=FALSE,grid=100,ub=2,...)

Arguments

y

The observed data. It is a vector of length at least 3.

sig

The standard deviations σ. If homoscedastic errors, sig is a single value. If heteroscedastic errors, sig is a vector of standard deviations having the same length as y.

z

z is the dependent variable.

x

x is user-defined grids where the regression function will be evaluated. FFT method is not applicable if x is given.

error

Error distribution types: (1) 'normal' for normal errors; (2) 'laplacian' for Laplacian errors; (3) 'snormal' for a special case of small normal errors.

bw

Specifies the bandwidth. It can be a single numeric value which has been pre-determined; or computed with the specific bandwidth selector: 'dnrd' to compute the rule-of-thumb plugin bandwidth as suggested by Fan (1991); 'dmise' to compute the plugin bandwidth by minimizing MISE; 'dboot1' to compute the bootstrap bandwidth selector without resampling (Delaigle and Gijbels, 2004a), which minimizing the MISE bootstrap bandwidth selectors; 'boot2' to compute the smoothed bootstrap bandwidth selector with resampling.

adjust

adjust the range there the regression function is to be evaluated. By default, adjust=1.

n

number of points where the regression function is to be evaluated.

from

the starting point where the regression functionF is to be evaluated.

to

the starting point where the regression function is to be evaluated.

cut

used to adjust the starting end ending points where the regression function is to be evaluated.

na.rm

is set to FALSE by default: no NA value is allowed.

grid

the grid number to search the optimal bandwidth when a bandwidth selector was specified in bw. Default value "grid=100".

ub

the upper boundary to search the optimal bandwidth, default value is "ub=2".

...

control

Details

FFT is currently not supported for nonparametric regression.

Value

An object of class “Decon”.

Author(s)

X.F. Wang wangx6@ccf.org

B. Wang bwang@jaguar1.usouthal.edu

References

Fan, J. and Truong, Y.K. (1993). Nonparametric regression with errors in variables. Annals of Statistics, 21(4), 1900-1925.

Delaigle, A. and Meister, A. (2007). Nonparametric regression estimation in the heteroscedastic errors-in-variables problem. Journal of the American Statistical Association, 102, 1416-1426.

Wang, X.F. and Wang, B. (2011). Deconvolution estimation in measurement error models: The R package decon. Journal of Statistical Software, 39(10), 1-24.

See Also

DeconPdf,DeconCdf.

Examples

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n <- 2000
x <- c(rnorm(n/2,2,1), rnorm(n/2, -2,1))
sig <- .8
u <- sig*rnorm(n)
w <- x+u
e <- rnorm(n, sd=0.2)
y <- x^2-2*x+e
bw1 <- bw.dboot1(w, sig)
# estimate the unknown density with measurement error
(m1 <-  DeconNpr(w, sig, y ,error="normal", from=0.9*min(x), to=0.9*max(x)))
# plot the results
plot(m1, col="red", lwd=3, lty=2, xlab="x", ylab="m(x)", main="", 
			zero.line=FALSE)
lines(ksmooth(x,y, kernel = "normal", 2, range.x=c(0.9*min(x),0.9*max(x))), 
			lwd=3, lty=1)
lines(ksmooth(w,y, kernel = "normal", 2, range.x=c(0.9*min(x),0.9*max(x))), 
			col="blue", lwd=3, lty=3)