DeconCPdf: Estimating conditional probability density function from data with measurement error

Description

To compute the conditional probability density function from data with measurement error. The measurement errors have to be homoscedastic.

Usage

DeconCPdf(y,sig,y0,error='normal',bw1='dboot1',bw2='nrd0',adjust=1,
	fft=FALSE,n=512,from,to,cut=3,na.rm=FALSE,grid=100,ub=2,tol=0,...)

Arguments

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

sig

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

The given conditional data point in the conditional density f(x|y=y0).

error

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

bw1

The bandwidth for the deconvolution density $f_{X}$ . 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.

bw2

The bandwidth for the kernel density $f_{Y}$ . It can be a single numeric value which has been pre-determined; or computed with the specific bandwidth selector: 'nrd0','nrd','ucv', 'bcv', and 'SJ' (see the "density" function in R).

adjust

adjust the range there the PDF is to be evaluated. By default, $a d j u s t = 1$ .

fft

To specify the method to compute the PDF. 'fft=FALSE' to compute directly; 'fft=TRUE' to compute the PDF by using the Fast Fourier Transformation.

number of points where the conditional PDF is to be evaluated.

from

the starting point where the conditional PDF is to be evaluated.

cut

used to adjust the starting end ending points where the conditional PDF 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".

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

tol

the parameter to avoid the estimate of f(y|x) too small. The default vaule is 0. It can not exceed 0.05.

...

control

Value

An object of class ``Decon''.

Details

If the number of points to be evaluated is too small (less than 32), a direct computing method is preferred. The current version can support up to $2^{2} 1$ points where the conditional PDF to be computed.

References

Fan, J. (1991). On the optimal rates of convergence for nonparametric deconvolution problems. The Annals of Statistics, 19, 1257-1272.

Wang XF, Ye D (2010). Conditional density estimation with measurement error. Technical Report.

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.

Examples

Run this code

# NOT RUN {
n <- 100
x <- c(rnorm(n/2,-2,1),rnorm(n/2,2,1))
sig <- .8
u <- rnorm(n,sd=sig)
w <- x+u

f1 <-  DeconCPdf(w,sig, y0=-2.5, error='normal')
#f2 <-  DeconCPdf(w,sig, y0=0, error='normal')
#f3 <-  DeconCPdf(w,sig, y0=2.5, error='normal')

#par(mfrow=c(2,2))
plot(density(w), main="f_w", xlab="w")
plot(f1, main="f1", xlab="x")
#plot(f2, main="f2", xlab="x")
#plot(f3, main="f3", xlab="x")

# }

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