Minimum Approximate Distance Estimate of Copula Density
made.copula(
x,
unif.mar = FALSE,
M = 30,
search = TRUE,
interval = NULL,
pseudo.obs = c("empirical", "mable"),
sig.level = 0.01
)An invisible mable object with components
m the given degree
p the estimated vector of mixture proportions
\(p = (p_0, \ldots, p_m)\)
with the given degree m
D the minimum distance at degree m
an n x d matrix of data values
marginals are all uniform (x contain pseudo observations)
or not.
d-vector of preselected or maximum model degrees
logical, whether to search optimal degrees between 0 and M
or not but use M as the given model degrees for the joint density.
a 2 by d matrix specifying the support/truncate interval of x,
if unif.mar=TRUE then interval is the unit hypercube
When unif.mar=FALSE, use "empirical" distribution to
create pseudo observations, or use "mable" of marginal cdfs to create
pseudo observations
significance level for p-value of change-point
With given model degrees m, the parameters p, the mixing
proportions of the beta distribution, are calculated as the minimizer of the
approximate \(L_2\) distance between the empirical distribution and
the Bernstein polynomial model. The optimal model degrees m are chosen by
a change-point method. The quadratic programming with linear constraints is
used to solve the problem.