pobs {copula} | R Documentation |
Compute the pseudo-observations for the given data matrix.
pobs(x, na.last = "keep", ties.method = , lower.tail = TRUE)
x |
n x d-matrix (or d-vector) of random variates to be converted to pseudo-observations. |
na.last, ties.method |
strings, passed to |
lower.tail |
|
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 (or vector) of the same dimensions as x
containing the
pseudo-observations.
## Simple definition of the function: pobs ## Draw from a multivariate normal distribution d <- 10 set.seed(1) P <- Matrix::nearPD(matrix(pmin(pmax(runif(d*d), 0.3), 0.99), ncol=d))$mat diag(P) <- rep(1, d) n <- 500 x <- MASS::mvrnorm(n, mu = rep(0, d), Sigma = P) ## Compute pseudo-observations (should roughly follow a Gauss ## copula with correlation matrix P) u <- pobs(x) plot(u[,5],u[,10], xlab=expression(italic(U)[1]), ylab=expression(italic(U)[2])) ## All components: pairwise plot pairs(u, gap=0, pch=".", labels=as.expression( sapply(1:d, function(j) bquote(italic(U[.(j)]))) ))