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Estimates in an admixture using Patra and Sen approach

Source: R/estim_PS.R
estim_PS.Rd

Estimation of both the weight and the distribution of the unknown component in an admixture model, by Patra and Sen approach. Remind that the admixture probability density function (pdf) l is given by l = p*f + (1-p)*g, where g is the known component of the two-component mixture, p is the unknown proportion of the unknown component distribution f. More information in 'Details' below concerning the estimation method.

Usage

estim_PS(
  samples,
  admixMod,
  method = c("fixed", "lwr.bnd", "cv"),
  c.n = 0.1 * log(log(length(samples))),
  folds = 10,
  reps = 1,
  cn.s = NULL,
  cn.length = 100,
  gridsize = 1200
)

Arguments

samples

Sample to be studied.

admixMod

An object of class admix_model, containing information about the known component distribution and its parameter(s).

method

One of 'lwr.bnd', fixed' or 'cv': depending on whether compute some lower bound of the mixing proportion, the estimate based on the value of 'c.n' or use cross-validation for choosing 'c.n' (tuning parameter).

c.n

(default to NULL) A positive number for the penalization, see reference below. If NULL, equals to 0.1*log(log(n)).

folds

(optional, default to 10) Number of folds used for cross-validation.

reps

(optional, default to 1) Number of replications for cross-validation.

cn.s

(optional) A sequence of 'c.n' to be used for cross-validation (vector of values). Default is equally spaced grid of 100 values between .001 x log(log(n)) and 0.2 x log(log(n)).

cn.length

(optional, default to 100) Number of equally spaced tuning parameter (between .001 x log(log(n)) and 0.2 x log(log(n))). Values to search from.

gridsize

(default to 600) Number of equally spaced points (between 0 and 1) to evaluate the distance function. Larger values are more computationally intensive but also lead to more accurate estimates.

Value

An object of class estim_PS, containing 10 attributes: 1) the number of samples studied (1 in this case); 2) the sample size; 3) the information about component distributions of the admixture model; 4) the estimation method 5patra and Sen here); 5) the estimated mixing weight (estimate of the unknown component proportion); 6) the estimated decontaminated CDF; 7) an object of the class 'dist.fun' (that gives the distance); 8) the tuning parameter 'c.n'; 9) the lower bound of the estimated mixing proportion (if such an option has been chosen); 10) the number of observations.

References

Patra RK, Sen B (2016). “Estimation of a two-component mixture model with applications to multiple testing.” Journal of the Royal Statistical Society Series B, 78(4), 869-893.

Author

Xavier Milhaud xavier.milhaud.research@gmail.com

Examples

## Simulate mixture data:
mixt1 <- twoComp_mixt(n = 800, weight = 0.33,
                      comp.dist = list("gamma", "exp"),
                      comp.param = list(list("shape" = 2, "scale" = 0.5),
                                        list("rate" = 0.25)))
data1 <- getmixtData(mixt1)
## Define the admixture model:
admixMod1 <- admix_model(knownComp_dist = mixt1$comp.dist[[2]],
                         knownComp_param = mixt1$comp.param[[2]])
## Estimation step:
estim_PS(samples = data1, admixMod = admixMod1, method = 'fixed')
#> Call:estim_PS(samples = data1, admixMod = admixMod1, method = "fixed")
#> 
#>  Estimate of the mixing weight (proportion of the unknown component distribution):  0.28