admix (version 2.4.2)

gaussianity_test: Gaussianity test in an admixture model

Description

Performs an hypothesis test to check for the gaussianity of the unknown mixture component. Recall that an admixture model has probability density function (pdf) l = p*f + (1-p)*g, where g is the known pdf and l is observed (others are unknown). This test requires optimization (to estimate the unknown parameters) as defined by Bordes & Vandekerkhove (2010), which means that the unknown mixture component must have a symmetric density.

Usage

gaussianity_test(
  sample,
  admixMod,
  conf_level = 0.95,
  ask_poly_param = FALSE,
  K = 3,
  s = 0.25,
  support = c("Real", "Integer", "Positive", "Bounded.continuous"),
  ...
)

Value

An object of class gaussianity_test, inherited class from "htest". Contains attributes like 1) the number of populations under study (1 in this case); 2) the sample size; 3) the information about the known component distribution; 4) the reject decision of the test; 5) the confidence level of the test, 6) the p-value of the test; 7) the value of the test statistic; 8) the variance of the test statistic at each order in the polynomial orthobasis expansion; 9) the selected rank (order) for the test statistic; 10) a list of estimates (mixing weight, mean and standard deviation of the Gaussian unknown distribution).

Arguments

sample

(numeric) The sample under study.

admixMod

An object of class admix_model, containing useful information about distributions and parameters.

conf_level

(default to 0.95) The confidence level. Equals 1-alpha, where alpha is the level of the test (type-I error).

ask_poly_param

(default to FALSE) If TRUE, ask the user to choose both the order 'K' of expansion coefficients in the orthonormal polynomial basis, and the penalization rate 's' involved on the penalization rule for the test.

K

(default to 3) If not asked (see the previous argument), number of coefficients considered for the polynomial basis expansion.

s

(in ]0,1/2[, default to 0.25) If not asked (see the previous argument), normalization rate involved in the penalization rule for model selection. See the reference below.

support

Support of the probability distributions, useful to choose the appropriate polynomial orthonormal basis. One of 'Real', 'Integer', 'Positive', or 'Bounded.continuous'.

...

Optional arguments to estim_BVdk.

Author

Xavier Milhaud

References

PommeretVandekerkhove2019admix

Examples

if (FALSE) {
####### Under the null hypothesis H0.
## Simulate mixture data:
mixt1 <- twoComp_mixt(n = 250, weight = 0.4,
                      comp.dist = list("norm", "exp"),
                      comp.param = list(list("mean" = -2, "sd" = 0.5),
                                        list("rate" = 1)))
data1 <- getmixtData(mixt1)
## Define the admixture models:
admixMod1 <- admix_model(knownComp_dist = mixt1$comp.dist[[2]],
                         knownComp_param = mixt1$comp.param[[2]])
## Performs the test:
gaussianity_test(sample = data1, admixMod = admixMod1,
                 conf_level = 0.95, K = 3, s = 0.1, support = "Real")
}