deamer.ro: Density estimation using an auxiliary sample of replicate...

In deamer: Deconvolution density estimation with adaptive methods for a variable prone to measurement error

Description

deamerRO performs a deconvolution estimation of the density of a noisy variable ('y') under the hypothesis of an unknown density of the noise using an auxiliary sample of replicate observations ("RO" for "replicate observations"). Therefore deamerRO requires two samples: one with single noisy observations and another with replicate noisy observations (see details).

Usage

deamerRO(y, replicates, grid.length = 100, from, to, na.rm = FALSE)

Arguments

y	Numeric. The vector of noisy observations.
replicates	Numeric. A 2-column matrix or 2-column numeric data-frame. Contains one replicate observation in each row. The number of rows does not need to match length(y).
grid.length	Numeric. Optional. The number of points of the grid the estimation is performed on. Defaults to 100.
from	Numeric. Optional. The lower bound of the grid the estimation is performed on. Defaults to min(y).
to	Numeric. Optional. The upper bound of the grid the estimation is performed on. Defaults to max(y).
na.rm	Logical. Optional. If na.rm=TRUE, NAs will be removed before estimation. Defaults to FALSE.

Details

The model is defined as y = x + e, where x and e both have unknown densities.
Replicate observations are defined as

z_1 = x + e_1

z_2 = x + e_2

The main underlying hypotheses are:

1. Homoscedasticity of the errors.

2. The errors e_1 and e_2 are independent.

3. The samples are independent.

4. Errors are symmetric, 0-mean variables.

5. Errors e, e_1 and e_2 have the same distribution.

Value

an object of class 'deamer'

Warning

• deamerRO is not implemented for heteroscedastic errors.

• Unlike deamerKE and deamerSE, deamerRO assumes the errors are centered around 0.

Note

deamerRO only allows for 2 replicates per observation for the moment (argument 'replicates' is a 2-column matrix or data-frame). Future versions should allow using more than 2.

Author(s)

Julien Stirnemann <[e-mail]>

References

Stirnemann JJ, Comte F, Samson A. Density estimation of a biomedical variable subject to measurement error using an auxiliary set of replicate observations. Statistics in medicine. 2012 May 17 [Epub ahead of print]

Comte F, Samson A, Stirnemann J. Deconvolution estimation of onset of pregnancy with replicate observations [Internet]. 2011 [cited 2011 Oct 25]. Available from: http://hal.archives-ouvertes.fr/hal-00588235_v2/

See Also

deamer, deamerKE, deamerSE, deamer-class

Examples

set.seed(123)
n=1000 #sample size of single noisy observtions
M=500 #sample size of replicate observations

rff=function(x){
  u=rbinom(x, 1, 0.5)
  X=u*rnorm(x, -2, 1)+(1-u)*rnorm(x,2,1)
  return(X)
}
x <- rff(n) #a mixed gaussian distribution

# true density function:
f.true=function(x) (0.5/(sqrt(2*pi)))*(exp(-0.5*(x+2)^2) + exp(-0.5*(x-2)^2))

e <- rnorm(n,0,0.5)
y <- x + e

x. <- rff(M)

e1 <- rnorm(M,0,0.5)
e2 <- rnorm(M,0,0.5)
rep<-data.frame(y1=x.+e1, y2=x.+e2)

est<-deamerRO(y, replicates=rep)
est

plot(est, lwd=2)
curve(f.true(x), add=TRUE, lwd=2, lty=3)
lines(density(y), lwd=2, lty=4)
legend("topleft", bty="n", lty=c(1,3,4), lwd=2, legend=c("deamerRO", "true density", 
       "kernel density\nof noisy obs."))

deamer documentation built on May 2, 2019, 12:36 p.m.