Estimation of the admixture parameters by Bordes & Vandekerkhove (2010)

Estimates parameters in an admixture model where the unknown component is assumed to have a symmetric density. More precisely, estimates the two parameters (mixture weight and location shift) in the admixture model with pdf: $$ \ell(x) = p f(x-\mu) + (1 - p) g(x), \quad x \in \mathbb{R}, $$ where $g$ is the known component, $p$ is the proportion and $f$ is the unknown component with symmetric density. The localization shift parameter is denoted $\mu$, and the component weight $p$. See the reference below for further details.

Usage

estim_BVdk(
  samples,
  admixMod,
  method = c("L-BFGS-B", "Nelder-Mead"),
  compute_var = FALSE
)

Arguments

samples: The observed sample under study.
admixMod: An object of class admix_model, with information about the known distribution and associated known parameter(s).
method: The method used throughout the optimization process, either 'L-BFGS-B' or 'Nelder-Mead' (see ?optim).
compute_var: (default to FALSE) A boolean that indicates whether one computes the variance of the estimators of unknown mixing proportions and location shift parameter.

Value

An object of class estim_BVdk, containing 8 attributes: 1) the number of sample under study (set to 1 here); 2) the sample size; 3) the information about mixture components (distributions and parameters); 4) the estimation method (Bordes and Vandekerkhove here, see the given reference); 5) the estimated mixing proportion (weight of the unknown component distribution); 6) the estimated location parameter of the unknown component distribution (with symmetric density); 7) the variance of the two estimators (respectively the mixing proportion and location shift); 8) the optimization method that was used.

References

Bordes L, Vandekerkhove P (2010). “Semiparametric two-component mixture model with a known component: An asymptotically normal estimator.” Mathematical Methods of Statistics, 19(1), 22–41. doi:10.3103/S1066530710010023 .

Author

Xavier Milhaud xavier.milhaud.research@gmail.com

Examples

if (FALSE) { # \dontrun{
## Simulate mixture data:
mixt1 <- twoComp_mixt(n = 200, weight = 0.4,
                      comp.dist = list("norm", "norm"),
                      comp.param = list(list("mean" = -2, "sd" = 0.5),
                                        list("mean" = 0, "sd" = 1)))
## Retrieves the mixture data:
data1 <- get_mixture_data(mixt1)
## Define the admixture model:
admixMod <- admix_model(knownComp_dist = mixt1$comp.dist[[2]],
                        knownComp_param = mixt1$comp.param[[2]])
## Perform the estimation of parameters in real-life:
ex <- estim_BVdk(samples = data1, admixMod = admixMod, method = 'L-BFGS-B')
print.estim_BVdk(ex)

## Second example:
mixt2 <- twoComp_mixt(n = 200, weight = 0.65,
                      comp.dist = list("norm", "exp"),
                      comp.param = list(list("mean" = -1, "sd" = 0.5),
                                        list("rate" = 1)))
data2 <- get_mixture_data(mixt2)
admixMod2 <- admix_model(knownComp_dist = mixt2$comp.dist[[2]],
                        knownComp_param = mixt2$comp.param[[2]])
## Perform the estimation of parameters in real-life:
ex <- estim_BVdk(samples = data2, admixMod = admixMod2, method = 'L-BFGS-B',
                 compute_var = TRUE)
print.estim_BVdk(ex)
} # }