`R/estimVarCov_empProcess.R`

`estimVarCov_empProcess.Rd`

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. |
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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)