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.

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

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). |
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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)). |

The value of the contrast.

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.

Xavier Milhaud xavier.milhaud.research@gmail.com

## 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)#> [1] 2.08444