admix (version 2.4.2)

admix_test: Equality test for the unknown components of admixture models

Description

Perform hypothesis test between unknown components of a list of admixture models, where 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, with g_i the known component density. The unknown quantities p_i and f_i are thus estimated, leading to the test given by the following null and alternative hypothesis: H0: f_i = f_j for all i != j against H1 : there exists at least i != j such that f_i differs from f_j. The test can be performed using two methods, either the comparison of coefficients obtained through polynomial basis expansions of the component densities, or by the inner-convergence property obtained using the IBM approach. See 'Details' below for further information.

Usage

admix_test(
  samples,
  admixMod,
  test_method = c("poly", "icv"),
  conf_level = 0.95,
  ...
)

Value

An object of class 'htest' containing the classical attributes of the latter class, as well as other attributes specific to the inherited object class. Usually, the test decision (reject the null hypothesis or not); the confidence level of the test (1-alpha, where alpha denotes the level of the test or equivalently the type-I error); the number of samples under study; the respective size of each sample; the information about known mixture components.

Arguments

samples

A list of the K (K > 0) samples to be studied, each one assumed to follow a mixture distribution.

admixMod

A list of objects of class admix_model, containing useful information about distributions and parameters of the contamination / admixture models under study.

test_method

The testing method to be applied. Can be either 'poly' (polynomial basis expansion) or 'icv' (inner convergence from IBM). The same testing method is performed between all samples. In the one-sample case, only 'poly' is available and the test is a gaussianity test. For further details, see section 'Details' below.

conf_level

The confidence level of the K-sample test.

...

Depending on the choice made by the user for the test method ('poly' or 'icv'), optional arguments to gaussianity_test or orthobasis_test (in case of 'poly'), and to IBM_k_samples_test in case of 'icv'.

Author

Xavier Milhaud

Details

For further details on implemented hypothesis tests, see the references hereafter. .

References

MilhaudPommeretSalhiVandekerkhove2024badmix MilhaudPommeretSalhiVandekerkhove2022admix PommeretVandekerkhove2019admix

Examples

####### Example with 2 samples
mixt1 <- twoComp_mixt(n = 380, 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 = 350, weight = 0.85,
                      comp.dist = list("norm", "norm"),
                      comp.param = list(list("mean" = -2, "sd" = 0.5),
                                        list("mean" = -1, "sd" = 1)))
data1 <- getmixtData(mixt1)
data2 <- getmixtData(mixt2)
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]])
admix_test(samples = list(data1,data2), admixMod = list(admixMod1,admixMod2),
           conf_level = 0.95, test_method = "poly", ask_poly_param = FALSE, support = "Real")