# DeconCPdf: Estimating conditional probability density function from data... In decon: Deconvolution Estimation in Measurement Error Models

## Description

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

## Usage

 ```1 2``` ```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

 `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. `y0` 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, adjust=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. `n` number of points where the conditional PDF is to be evaluated. `from` the starting point where the conditional PDF is to be evaluated. `to` 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". `ub` 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

## 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 2^21 points where the conditional PDF to be computed.

## Value

An object of class “Decon”.

## 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.

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.

## See Also

`DeconPdf`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```n <- 1000 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") ```

decon documentation built on May 2, 2019, 3:46 p.m.