Estimate the variance-covariance matrix of some given empirical process, based on the Donsker correlation. Compute Donsker correlation between two time points (x,y) for some given empirical process with R code (another implementation in C++ is also available to speed up this computation).

estimVarCov_empProcess(
x,
y,
obs.data,
known.p = NULL,
comp.dist = NULL,
comp.param = NULL
)

## Arguments

x First time point considered for the computation of the correlation given the empirical process. Second time point considered for the computation of the correlation given the same empirical process. Sample that permits to estimate the cumulative distribution function (cdf). NULL by default (only useful to compute the exact Donsker correlation). The component weight dedicated to the unknown mixture component if available (in case of simulation studies) NULL by default (only useful to compute the exact Donsker correlation). Otherwise, a list with two elements corresponding to component distributions (specified with R native names for these distributions) involved in the admixture model. All elements must be specified, for instance list(f='norm', g='norm'). NULL by default (only useful to compute the exact Donsker correlation). Otherwise, 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. All elements must be specified, for instance list(f=NULL, g=list(mean=0,sd=1)).

## Value

The estimated variance-covariance matrix.

## Author

Xavier Milhaud xavier.milhaud.research@gmail.com

## Examples

## Simulate data:
list.comp <- list(f1 = 'norm', g1 = 'norm')
list.param <- list(f1 = list(mean = 12, sd = 0.4),
g1 = list(mean = 16, sd = 0.7))
obs.data <- rsimmix(n=2500, unknownComp_weight=0.5, comp.dist=list.comp, comp.param= list.param)
## Compute the variance-covariance matrix of the corresponding empirical process:
t <- seq(from = min(obs.data$mixt.data), to = max(obs.data$mixt.data), length = 50)
S2 <- sapply(t, function(s1) {
sapply(t, function(s2) {
estimVarCov_empProcess(x = s1, y = s2, obs.data = obs.data\$mixt.data) })
})
lattice::wireframe(S2) 