estimVarCov_empProcess {admix} | R Documentation |

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
)
```

`x` |
First time point considered for the computation of the correlation given the empirical process. |

`y` |
Second time point considered for the computation of the correlation given the same empirical process. |

`obs.data` |
Sample that permits to estimate the cumulative distribution function (cdf). |

`known.p` |
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) |

`comp.dist` |
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'). |

`comp.param` |
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)). |

The estimated variance-covariance matrix.

Xavier Milhaud xavier.milhaud.research@gmail.com

```
## 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)
```

[Package *admix* version 2.1-2 Index]