Estimation of the two parameters (mixture weight as well as 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 thus denoted mu, and the component weight p. See 'Details' below for further information.

BVdk_estimParam(
  data,
  method = c("L-BFGS-B", "Nelder-Mead"),
  comp.dist,
  comp.param
)

Arguments

data

The observed sample under study.

method

The method used throughout the optimization process, either 'L-BFGS-B' or 'Nelder-Mead' (see ?optim).

comp.dist

A list with two elements corresponding to component distributions (specified with R native names for these distributions) involved in the admixture model. Unknown elements must be specified as 'NULL' objects, e.g. when 'f' is unknown: list(f=NULL, g='norm').

comp.param

A list with two elements corresponding to the parameters of the component distributions, each element being a list itself. The names used in this list must correspond to the native R argument names for these distributions. Unknown elements must be specified as 'NULL' objects, e.g. if 'f' is unknown: list(f=NULL, g=list(mean=0,sd=1)).

Value

A numeric vector with the two estimated parameters (proportion first, and then location shift).

Details

Parameters are estimated by minimization of the contrast function, where the contrast is defined in Bordes, L. and Vandekerkhove, P. (2010); Semiparametric two-component mixture model when a component is known: an asymptotically normal estimator; Math. Meth. Stat.; 19, pp. 22--41.

Author

Xavier Milhaud xavier.milhaud.research@gmail.com

Examples

## Simulate data: list.comp <- list(f = 'norm', g = 'norm') list.param <- list(f = list(mean = 3, sd = 0.5), g = list(mean = 0, sd = 1)) data1 <- rsimmix(n = 400, unknownComp_weight = 0.8, list.comp, list.param)[['mixt.data']] ## Perform the estimation of parameters in real-life: list.comp <- list(f = NULL, g = 'norm') list.param <- list(f = NULL, g = list(mean = 0, sd = 1)) BVdk_estimParam(data1, method = 'L-BFGS-B', list.comp, list.param)
#> [1] 0.8136978 2.9967161