Provide the decontaminated cumulative distribution function (CDF) of the unknown component in an admixture model

Description

Estimate the decontaminated CDF of the unknown component in the admixture model under study, after inversion of the admixture cumulative distribution function. Recall that an admixture model follows the cumulative distribution function (CDF) L, where L = p*F + (1-p)*G, with g a known CDF and p and f unknown quantities.

Usage

decontamin_cdf_unknownComp(sample1, comp.dist, comp.param, estim.p)

Arguments

 sample1 Observations of the sample under study. comp.dist A list with two elements corresponding to the component distributions (specified with R native names for these distributions) involved in the admixture model. The two elements refer to the unknown and known components of the admixture model, If there are unknown elements, they must be specified as 'NULL' objects (e.g. 'comp.dist' could be set to list(f1=NULL, g1='norm')). comp.param A list with two elements corresponding to the parameters of the component distributions, each element being a list itself. The names used in this list must correspond to the native R argument names for these distributions. The two elements refer to the parameters of unknown and known components of the admixture model. If there are unknown elements, they must be specified as 'NULL' objects (e.g. 'comp.param' could be set to list(f1=NULL, g1=list(mean=0,sd=1))). estim.p The estimated weight of the unknown component distribution, related to the proportion of the unknown component in the admixture model studied.

Details

The decontaminated CDF is obtained by inverting the admixture CDF, given by L = p*F + (1-p)*G, to isolate the unknown component F after having estimated p. This means that F = (1/hat(p)) * (hat(L)-(1-p)*G).

Value

The decontaminated CDF F of the admixture model, as an of class 'stepfun' (step function).

Author(s)

Xavier Milhaud xavier.milhaud.research@gmail.com

Examples

####### Continuous support:
## Simulate data:
list.comp <- list(f1 = 'norm', g1 = 'norm',
f2 = 'norm', g2 = 'norm')
list.param <- list(f1 = list(mean = 3, sd = 0.5), g1 = list(mean = 0, sd = 1),
f2 = list(mean = 3, sd = 0.5), g2 = list(mean = 5, sd = 2))
sample1 <- rsimmix(n=3500, unknownComp_weight=0.5, comp.dist = list(list.comp\$f1,list.comp\$g1),
comp.param=list(list.param\$f1,list.param\$g1))
sample2 <- rsimmix(n=3000, unknownComp_weight=0.7, comp.dist = list(list.comp\$f2,list.comp\$g2),
comp.param=list(list.param\$f2,list.param\$g2))
## Estimate the mixture weight in each of the sample in real-life setting:
list.comp <- list(f1 = NULL, g1 = 'norm',
f2 = NULL, g2 = 'norm')
list.param <- list(f1 = NULL, g1 = list(mean = 0, sd = 1),
f2 = NULL, g2 = list(mean = 5, sd = 2))
estimate <- IBM_estimProp(sample1[['mixt.data']], sample2[['mixt.data']], comp.dist = list.comp,
comp.param = list.param, with.correction = FALSE, n.integ = 1000)
## Determine the decontaminated version of the unknown CDF by inversion:
decontamin_cdf_unknownComp(sample1 = sample1[['mixt.data']],
comp.dist = list.comp[1:2], comp.param = list.param[1:2],
estim.p = estimate\$prop.estim)
####### Countable discrete support:
list.comp <- list(f1 = 'pois', g1 = 'pois',
f2 = 'pois', g2 = 'pois')
list.param <- list(f1 = list(lambda = 3), g1 = list(lambda = 2),
f2 = list(lambda = 3), g2 = list(lambda = 4))
sample1 <- rsimmix(n=6000, unknownComp_weight=0.6, comp.dist = list(list.comp\$f1,list.comp\$g1),
comp.param=list(list.param\$f1,list.param\$g1))
sample2 <- rsimmix(n=4500, unknownComp_weight=0.8, comp.dist = list(list.comp\$f2,list.comp\$g2),
comp.param=list(list.param\$f2,list.param\$g2))
## Estimate the mixture weight in each of the sample in real-life setting:
list.comp <- list(f1 = NULL, g1 = 'pois',
f2 = NULL, g2 = 'pois')
list.param <- list(f1 = NULL, g1 = list(lambda = 2),
f2 = NULL, g2 = list(lambda = 4))
estimate <- IBM_estimProp(sample1[['mixt.data']], sample2[['mixt.data']], comp.dist = list.comp,
comp.param = list.param, with.correction = FALSE, n.integ = 1000)
decontamin_cdf_unknownComp(sample1 = sample1[['mixt.data']],
comp.dist = list.comp[1:2], comp.param = list.param[1:2],
estim.p = estimate\$prop.estim)
####### Finite discrete support:
list.comp <- list(f1 = 'multinom', g1 = 'multinom',
f2 = 'multinom', g2 = 'multinom')
list.param <- list(f1 = list(size=1, prob=c(0.3,0.4,0.3)), g1 = list(size=1, prob=c(0.6,0.3,0.1)),
f2 = list(size=1, prob=c(0.3,0.4,0.3)), g2 = list(size=1, prob=c(0.2,0.6,0.2)))
sample1 <- rsimmix(n=8000, unknownComp_weight=0.6, comp.dist = list(list.comp\$f1,list.comp\$g1),
comp.param=list(list.param\$f1,list.param\$g1))
sample2 <- rsimmix(n=6000, unknownComp_weight=0.8, comp.dist = list(list.comp\$f2,list.comp\$g2),
comp.param=list(list.param\$f2,list.param\$g2))
list.comp <- list(f1 = NULL, g1 = 'multinom',
f2 = NULL, g2 = 'multinom')
list.param <- list(f1 = NULL, g1 = list(size=1, prob=c(0.6,0.3,0.1)),
f2 = NULL, g2 = list(size=1, prob=c(0.2,0.6,0.2)))
estimate <- IBM_estimProp(sample1[['mixt.data']], sample2[['mixt.data']], comp.dist = list.comp,
comp.param = list.param, with.correction = FALSE, n.integ = 1000)
decontamin_cdf_unknownComp(sample1 = sample1[['mixt.data']],
comp.dist = list.comp[1:2], comp.param = list.param[1:2],
estim.p = estimate\$prop.estim)