npdenest {decon}

Estimating probability density function from data with unknown measurement error

Description

To compute the probability density function from data contaminated with measurement error. The measurement error type is unknown.

Usage

 npdenest(w, e, bw, adjust = 1, n = 512, from, to, cut = 3, na.rm = FALSE,...) 

Arguments

w

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

e

Observed vector of measurement errors.

bw

Smoothing parameter.

adjust

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

n

number of points where the PDF is to be evaluated.

from

the starting point where the PDF is to be evaluated.

to

the starting point where the PDF is to be evaluated.

cut

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

na.rm

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

...

controls

Details

The optimal bandwidth is selected by minimizing abs(Var(f.hat)+Var(E)-Var(Y)).

Value

An object of class “Decon”.

References

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

DeconCdf, DeconNpr, DeconCPdf.

Examples

 n1 <- 1500
 x1 <- rnorm(n1, sd=1)
 sig1 <- .5
 u1 <- ifelse(runif(n1) > 0.5, 1, -1) * rexp(n1,rate=1/sig1)
 w1 <- x1+u1
 ## The rule-of-thumb method may not be accurate, 
 ## you may try the bootstrap method
 bw1 <- bw.dnrd(w1,sig=sig1, error="laplacian")
 (f1 <-  DeconPdf(w1,sig1,error='laplacian',bw=bw1, fft=TRUE))
 (f2 <-  npdenest(w1, u1))

 # plot the results
 par(mfrow=c(1,1))
 plot(f1,  col="red", lwd=3, lty=2, xlab="x", ylab="f(x)", main="")
 lines(density(x1, from=min(w1), to=max(w1)), lwd=3, lty=1)
 lines(density(w1), col="blue", lwd=3, lty=3)
 lines(f2, col='red', lty=1,lwd=3)