admix (version 2.3.4)

admix_estim: Estimate the unknown parameters of the admixture model(s)

Description

Estimate the component weights, the location shift parameter (in case of a symmetric unknown component density), and the unknown component distribution using different estimation techniques. We remind that the i-th admixture model has probability density function (pdf) l_i such that: l_i = p_i * f_i + (1-p_i) * g_i, where g_i is the known component density. The unknown quantities p_i and f_i then have to be estimated.

Usage

admix_estim(samples, admixMod, est_method = c("PS", "BVdk", "IBM"), ...)

Value

An object of class admix_estim, containing at least 5 attributes: 1) the number of samples under study; 2) the information about the mixture components (distributions and parameters); 3) the sizes of the samples; 4) the chosen estimation technique (one of 'BVdk', 'PS' or 'IBM'); 5) the estimated mixing proportions (weights of the unknown component distributions in the mixture model). In case of 'BVdk' estimation, one additional attribute corresponding to the estimated location shift parameter is included.

Arguments

samples

A list of the K (K>0) samples to be studied, all following admixture distributions.

admixMod

A list of objects of class admix_model, containing useful information about distributions and parameters.

est_method

The estimation method to be applied. Can be one of 'BVdk' (Bordes and Vandekerkhove estimator), 'PS' (Patra and Sen estimator), or 'IBM' (Inversion Best-Matching approach) in the continuous case (continuous random variable). Only 'IBM' for discrete random variables. The same estimation method is performed on each sample if several samples are provided.

...

Optional arguments to estim_PS, estim_BVdk or estim_IBM depending on the choice made by the user for the estimation method.

Author

Xavier Milhaud

Details

For further details on the different estimation techniques, see references below on i) Patra and Sen estimator ; ii) Bordes and Vandekerkhove estimator ; iii) Inversion Best-Matching approach. Important note: estimation by 'IBM' requires at least two samples at hand, and provides unbiased estimators only if the distributions of unknown components are equal (meaning that it requires to perform previously this test between the pairs of samples, see ?admix_test).

References

PatraSen2016admix BordesDelmasVandekerkhove2006admix BordesVandekerkhove2010admix MilhaudPommeretSalhiVandekerkhove2024aadmix

Examples

## Simulate mixture data:
mixt1 <- twoComp_mixt(n = 300, weight = 0.7,
                      comp.dist = list("norm", "norm"),
                      comp.param = list(list("mean" = -2, "sd" = 0.5),
                                        list("mean" = 0, "sd" = 1)))
mixt2 <- twoComp_mixt(n = 250, weight = 0.85,
                      comp.dist = list("norm", "exp"),
                      comp.param = list(list("mean" = -2, "sd" = 0.5),
                                        list("rate" = 1)))
data1 <- getmixtData(mixt1)
data2 <- getmixtData(mixt2)
## Define the admixture models:
admixMod1 <- admix_model(knownComp_dist = mixt1$comp.dist[[2]],
                         knownComp_param = mixt1$comp.param[[2]])
admixMod2 <- admix_model(knownComp_dist = mixt2$comp.dist[[2]],
                         knownComp_param = mixt2$comp.param[[2]])
# Estimation by different methods:
admix_estim(samples=list(data1), admixMod=list(admixMod1), est_method = "BVdk")
admix_estim(samples=list(data1,data2), admixMod=list(admixMod1,admixMod2), est_method = "PS")
admix_estim(samples=list(data1,data2), admixMod=list(admixMod1,admixMod2), est_method = "IBM")