bw.dnrd {decon} | R Documentation |
A rule of thumb bandwidth selection in denconvolution problems
Description
To compute the optimal bandwidth using the rule-of-thumb methods based on theorem 1 and theorem 2 of Fan (1991).
Usage
bw.dnrd(y,sig,error='normal')
Arguments
y |
The observed data. It is a vector of length at least 3. |
sig |
The standard deviation(s) |
error |
Error distribution types: 'normal', 'laplacian' for normal and Laplacian errors, respectively. |
Details
The current version approximate the
second term in the MISE by assuming that X
is
normally distributed. In the case of heteroscedastic error, the variance was approximated by the arithematic mean of the variances of U
.
Value
the selected bandwidth.
Author(s)
X.F. Wang wangx6@ccf.org
B. Wang bwang@jaguar1.usouthal.edu
References
Fan, J. (1991). On the optimal rates of convergence for nonparametric deconvolution problems. The Annals of Statistics, 19, 1257-1272.
Fan, J. (1992). Deconvolution with supersmooth distributions. The Canadian Journal of Statistics, 20, 155-169.
Stefanski, L. and Carroll, R. J. (1990). Deconvoluting kernel density estimators. Statistics, 21, 169-184.
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
bw.dmise
, bw.dboot1
, bw.dboot2
.
Examples
n <- 1000
x <- c(rnorm(n/2,-2,1),rnorm(n/2,2,1))
## the case of homoscedastic normal error
sig <- .8
u <- rnorm(n, sd=sig)
w <- x+u
bw.dnrd(w,sig=sig)
## the case of homoscedastic laplacian error
sig <- .8
## generate laplacian errors
u <- ifelse(runif(n) > 0.5, 1, -1) * rexp(n,rate=1/sig)
w <- x+u
bw.dnrd(w,sig=sig,error='laplacian')
## the case of heteroscedastic normal error
sig <- runif(n, .7, .9)
u <- sapply(sig, function(x) rnorm(1, sd=x))
w <- x+u
bw.dnrd(w,sig=sig,error='normal')