Pseudo-Observations
Compute the pseudo-observations for the given data matrix.
pobs( x, na.last = "keep", ties.method = eval(formals(rank)$ties.method), lower.tail = TRUE )
Given n realizations
x_i=(x_{i1},...,x_{id}),
i in {1,...,n} of a random vector X,
the pseudo-observations are defined via u_{ij}=r_{ij}/(n+1) for
i in {1,...,n} and j in
{1,...,d}, where r_{ij} denotes the rank of x_{ij} among all
x_{kj}, k in {1,...,n}. The
pseudo-observations can thus also be computed by component-wise applying the
empirical distribution functions to the data and scaling the result by
n/(n+1). This asymptotically negligible scaling factor is used to
force the variates to fall inside the open unit hypercube, for example, to
avoid problems with density evaluation at the boundaries. Note that
pobs(, lower.tail=FALSE) simply returns 1-pobs().
matrix of the same dimensions as x containing the
pseudo-observations.
This function is borrowed from the
copula() package.
Marius Hofert
## Simple definition of the function: pobs ## simulate data from a multivariate normal distribution library(mvtnorm) set.seed(123) Sigma <- matrix(c(2, 1, -0.2, 1, 1, 0.3, -0.2, 0.3, 0.5), 3, 3) mu <- c(-3, 2, 1) dat <- rmvnorm(500, sigma = Sigma) pairs(dat) # plot observations ## compute pseudo-observations for copula inference udat <- pobs(dat) pairs(udat) # estimate vine copula model fit <- RVineStructureSelect(udat, familyset = c(1, 2))
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