Performs an hypothesis test to check for the gaussianity of the unknown mixture component, given that the known component has support on the real line. 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(
samples,
admixMod,
conf_level = 0.95,
ask_poly_param = FALSE,
K = 3,
s = 0.25,
support = c("Real", "Integer", "Positive", "Bounded.continuous"),
...
)Arguments
- samples
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
(K > 0, 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.
Value
An object of class gaussianity_test, containing 10 elements: 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).
Details
Extensions to the case of non-Gaussian known components can be overcome thanks to basic transformations using cdf.
References
Pommeret D, Vandekerkhove P (2019). “Semiparametric density testing in the contamination model.” Electronic Journal of Statistics, 4743--4793. doi:10.1214/19-EJS1650 .
Author
Xavier Milhaud xavier.milhaud.research@gmail.com
Examples
####### 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(samples = data1, admixMod = admixMod1,
conf_level = 0.95, K = 3, s = 0.1, support = "Real")
#> Call:gaussianity_test(samples = data1, admixMod = admixMod1, conf_level = 0.95,
#> K = 3, s = 0.1, support = "Real")
#>
#> Is the null hypothesis (gaussian unknown component distribution) rejected? No
#> Test p-value: 0.975