BVdk_contrast {admix}

Contrast as defined in Bordes & Vandekerkhove (2010)

Description

Compute the contrast as defined in Bordes & Vandekerkhove (2010) (see below in section 'Details'), needed for optimization purpose. Remind that one considers an admixture model with symmetric unknown density, i.e. l(x) = p*f(x-mu) + (1-p)*g(x), where l denotes the probability density function (pdf) of the mixture with known component pdf g, p is the unknown mixture weight, f relates to the unknown symmetric component pdf f, and mu is the location shift parameter.

Usage

BVdk_contrast(param, data, h, comp.dist, comp.param)

Arguments

param

Numeric vector of two elements, corresponding to the two parameters (first the unknown component weight, and then the location shift parameter of the symmetric unknown component distribution).

data

Numeric vector of observations following the admixture model given by the pdf l.

h

Width of the window used in the kernel estimations.

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)).

Details

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.

Value

The value of the contrast.

Author(s)

Xavier Milhaud [e-mail]

Examples

## Simulate data:
comp.dist <- list(f = 'norm', g = 'norm')
comp.param <- list(f = list(mean = 3, sd = 0.5), g = list(mean = 0, sd = 1))
data1 <- rsimmix(n = 1000, unknownComp_weight = 0.6, comp.dist, comp.param)[['mixt.data']]
## Compute the contrast value for some given parameter vector in real-life framework:
comp.dist <- list(f = NULL, g = 'norm')
comp.param <- list(f = NULL, g = list(mean = 0, sd = 1))
BVdk_contrast(c(0.3,2), data1, density(data1)$bw, comp.dist, comp.param)