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: l(x) = p*f(x-mu) + (1-p)*g(x), x in 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, containing useful information about distributions and parameters.
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 symetric 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

## 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 <- getmixtData(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:
estim_BVdk(samples = data1, admixMod = admixMod, method = 'L-BFGS-B')
#> Warning: Estimation by 'BVdk' assumes the unknown component distribution
#>   to have a symmetric probability density function.
#> 
#> Call:estim_BVdk(samples = data1, admixMod = admixMod, method = "L-BFGS-B")
#> 
#> Estimated mixing proportion:  0.3997622 
#> Estimated location parameter:  -1.986474 
#> Variance of the mixing proportion estimator:  NA 
#> Variance of the location shift estimator:  NA 
#> 

## 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 <- getmixtData(mixt2)
admixMod2 <- admix_model(knownComp_dist = mixt2$comp.dist[[2]],
                        knownComp_param = mixt2$comp.param[[2]])
## Perform the estimation of parameters in real-life:
estim_BVdk(samples = data2, admixMod = admixMod2, method = 'L-BFGS-B',
           compute_var = TRUE)
#> Warning: Estimation by 'BVdk' assumes the unknown component distribution
#>   to have a symmetric probability density function.
#> 
#> Call:estim_BVdk(samples = data2, admixMod = admixMod2, method = "L-BFGS-B", 
#>     compute_var = TRUE)
#> 
#> Estimated mixing proportion:  0.6165552 
#> Estimated location parameter:  -1.06661 
#> Variance of the mixing proportion estimator:  0.001413177 
#> Variance of the location shift estimator:  0.002412356 
#>