made.copula: Minimum Approximate Distance Estimate of Copula Density

In mable: Maximum Approximate Bernstein/Beta Likelihood Estimation

Minimum Approximate Distance Estimate of Copula Density

Description

Minimum Approximate Distance Estimate of Copula Density

Usage

made.copula(
  x,
  unif.mar = FALSE,
  M = 30,
  search = TRUE,
  interval = NULL,
  pseudo.obs = c("empirical", "mable"),
  sig.level = 0.01
)

Arguments

x	an n x d matrix of data values
unif.mar	marginals are all uniform (x contain pseudo observations) or not.
M	d-vector of preselected or maximum model degrees
search	logical, whether to search optimal degrees between 0 and M or not but use M as the given model degrees for the joint density.
interval	a 2 by d matrix specifying the support/truncate interval of x, if unif.mar=TRUE then interval is the unit hypercube
pseudo.obs	When unif.mar=FALSE, use "empirical" distribution to create pseudo observations, or use "mable" of marginal cdfs to create pseudo observations
sig.level	significance level for p-value of change-point

Details

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.

Value

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

mable documentation built on Oct. 1, 2024, 9:06 a.m.