pobs: Pseudo-Observations

In VineCopula: Statistical Inference of Vine Copulas

Pseudo-Observations

Description

Compute the pseudo-observations for the given data matrix.

Usage

pobs(
  x,
  na.last = "keep",
  ties.method = eval(formals(rank)$ties.method),
  lower.tail = TRUE
)

Arguments

x	n\times d-matrix of random variates to be converted to pseudo-observations.
na.last, ties.method	are passed to rank(); see there.
lower.tail	logical() which, if FALSE, returns the pseudo-observations when applying the empirical marginal survival functions.

Details

Given n realizations \bm{x}_i=(x_{i1},\dots,x_{id})^T, i\in\{1,\dots,n\} of a random vector \bm{X}, the pseudo-observations are defined via u_{ij}=r_{ij}/(n+1) for i\in\{1,\dots,n\} and j\in\{1,\dots,d\}, where r_{ij} denotes the rank of x_{ij} among all x_{kj}, k\in\{1,\dots,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().

Value

matrix of the same dimensions as x containing the pseudo-observations.

Note

This function is adapted from the copula package.

Author(s)

Marius Hofert, Thomas Nagler

Examples

## 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))

VineCopula documentation built on Sept. 11, 2024, 5:26 p.m.