Description Usage Arguments Details Value Warning Author(s) References See Also Examples

The `deamer`

class defines the objects produced by `deamer.default`

or any of
`deamerKE`

, `deamerSE`

or `deamerRO`

. Objects of class `deamer`

can be used in generic functions such as `plot`

, `print`

and `predict`

.

The default function `deamer`

assumes the user is familiar with all 3 methods "se", "ke" and "ro" (see `deamer`

and details), whereas method-specific wrappers
`deamerKE`

, `deamerSE`

, `deamerRO`

are intended for those who are not.

1 2 3 4 5 |

`y` |
Numeric. The vector of noisy observations. |

`errors` |
Numeric. The vector of the auxiliary sample of errors.
Does not need to be the same length as |

`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 |

`mu` |
Numeric. The (known) mean of the noise. Defaults to zero. |

`sigma` |
Numeric. The (known) standard deviation of the noise if |

`noise.type` |
Character. Defines the type of density for the noise. Only |

`method` |
Character. Only one of |

`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 |

`to` |
Numeric. Optional. The upper bound of the grid the estimation is performed on. Defaults to |

`na.rm` |
Logical. Optional. If |

`object` |
An object of class |

`newdata` |
Numeric vector (possibly single valued). |

`...` |
Further arguments for generic functions |

The estimation method is chosen according to the `method`

argument.
For known density noise, `method="ke"`

and arguments `'mu'`

and `'sigma'`

should be supplied. For estimation with an auxiliary sample of errors `method="se"`

and argument
`'errors'`

should be supplied. For estimation with an auxiliary sample of replicates,
`method="ro"`

and argument `'replicates'`

should be supplied.
For further details on each of these models, see `deamer`

and functions
`deamerKE`

, `deamerSE`

and `deamerRO`

respectively.
These functions are wrappers for deamer.default and have a more straightforward usage.

`y` |
The input vector. |

`f` |
The deconvolution estimate of the density of |

`n` |
Length of input vector. |

`M` |
Sample size of pure errors (argument |

`method` |
The method of estimation. Possible values: |

`mu` |
The mean of the error density for |

`sigma` |
The standard deviation (resp. scale parameter) of the error density for |

`supp` |
The grid of values used for estimation. |

`m` |
The estimated parameter for adaptive model selection. |

`ahat` |
Values of the estimated projection coefficients using Fast Fourier Transform. |

Generic function `predict`

yields a vector of predictions.

Heteroscedastic errors are not supported in any of `deamerKE`

, `deamerSE`

, `deamerRO`

.

Julien Stirnemann <j.stirnemann@gmail.com>

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, Lacour C. Data-driven density estimation in the presence of additive
noise with unknown distribution. Journal of the Royal Statistical Society:
Series B (Statistical Methodology). 2011 Sep 1;73(4):601-27.

Comte F, Rozenholc Y, Taupin M-L. Penalized Contrast Estimator for Adaptive
Density Deconvolution. The Canadian Journal of Statistics /
La Revue Canadienne de Statistique. 2006; 34(3):431-52.

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/

`deamer`

, `deamerKE`

, `deamerRO`

, `deamerSE`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | ```
#this example based on simulated data presents each method implemented in deamer.
#the deamer function is presented but the wrappers deamerKE, deamerRO
#and deamerSE would yield the same results.
set.seed(12345)
n=1000; M=500
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 <- rlaplace(n, 0, 0.5) # laplace noise
y <- x + e # observations with additive noise
eps <- rlaplace(M, 0, 0.5) # a sample of pure errors for method="se"
# a 2-column matrix of replicate noisy observations for method="ro"
rep <- matrix(rep(rff(M),each=2)+rlaplace(2*M,0,0.5), byrow=TRUE, ncol=2)
#estimation with known error
# the same as deamerKE(y, noise.type="laplace", sigma=0.5)
est.ke <- deamer(y, noise.type="laplace", sigma=0.5, method="ke")
#will generate a warning since we are assuming mu=0
est.ke
#estimation with an auxiliary sample of errors
# the same as deamerSE(y, errors=eps)
est.se <- deamer(y, errors=eps, method="se")
est.se
#estimation with replicate noisy observations
# the same as deamerRO(y, replicates=rep)
est.ro <- deamer(y, replicates=rep, method="ro")
est.ro
curve(f.true(x), from=-6, to=6,lwd=2, lty=2)
lines(est.ke, lwd=1, col="green3")
lines(est.se, lwd=1, col="blue2")
lines(est.ro, lwd=1, col="orange")
legend("topright", lty=c(2,1,1,1), col=c("black", "green3", "blue2","orange"),
legend=c("true density", "method='ke'", "method='se'", "method='ro'"),
bty='n')
#compare predictions for each method for newx
newx=c(-2,0,2)
rbind(
predict(est.ke, newdata=newx),
predict(est.se, newdata=newx),
predict(est.ro, newdata=newx)
) -> preds
dimnames(preds)<-list(c("ke","se","ro"),newx)
#predictions are made at newdata
preds
``` |

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