decon (version 1.3-4)

bw.dmise: The MISE based plug-in bandwidth selection

Description

To compute the optimal bandwidth using the plug-in methods by minimizing MISE.

Usage

bw.dmise(y,sig,error="normal",kernel="support",grid=100,ub=2)

Arguments

y

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

sig

The standard deviation(s) \(\sigma\). For homoscedastic errors, \(sig\) is a single value. Otherwise, \(sig\) is a vector of variances having the same length as \(y\).

error

Error distribution types: 'normal', 'laplacian' for normal and Laplacian errors, respectively.

kernel

Kernel type: 'support' for support kernel; and 'normal' for Gaussian kernel.

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".

Value

the selected bandwidth.

Details

The current version approximate the second term in the MISE by assuming that \(X\) is normally distributed.

References

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.dnrd, bw.dboot1, bw.dboot2.

Examples

# NOT RUN {
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.dmise(w,sig=sig,error='normal');
## The small error case
sig <- .25
u <- rnorm(n, sd=sig)
w <- x+u
bw.dmise(w,sig=sig,kernel='normal',error='normal');

## the case of homoscedastic laplacian error
sig <- .8
## generate laplacian error
u <- ifelse(runif(n) > 0.5, 1, -1) * rexp(n,rate=1/sig)
w <- x+u
bw.dmise(w,sig=sig,error='laplace')

## the case of heteroscedastic normal error
sig <- runif(n, .7, .9)
u <- sapply(sig, function(x) rnorm(1, sd=x))
w <- x+u
bw.dmise(w,sig=sig,kernel='support',error='normal')

# }