mable.hellcorr function

Estimate of Hellinger Correlation between two random variables and Bootstrap

mable.hellcorr(
  x,
  unif.mar = FALSE,
  pseudo.obs = c("empirical", "mable"),
  M0 = c(1, 1),
  M = c(30, 30),
  search = TRUE,
  mar.deg = TRUE,
  high.dim = FALSE,
  interval = cbind(0:1, 0:1),
  B = 200L,
  conf.level = 0.95,
  integral = TRUE,
  controls = mable.ctrl(sig.level = 0.05),
  progress = FALSE
)

hellcorr(
  x,
  unif.mar = FALSE,
  pseudo.obs = c("empirical", "mable"),
  M0 = c(1, 1),
  M = c(30, 30),
  search = TRUE,
  mar.deg = TRUE,
  high.dim = FALSE,
  interval = cbind(0:1, 0:1),
  B = 200L,
  conf.level = 0.95,
  integral = TRUE,
  controls = mable.ctrl(sig.level = 0.05),
  progress = FALSE
)

Arguments

• x: an n x 2 data matrix of observations of the two random variables

• unif.mar: logical, whether all the marginals distributions are uniform or not. If not the pseudo observations will be created using empirical or mable

  marginal distributions.

• pseudo.obs: "empirical": use empirical distribution to form pseudo, observations, or "mable": use mable of marginal cdfs to form pseudo observations

• M0: a nonnegative integer or a vector of d nonnegative integers specify starting candidate degrees for searching optimal degrees.

• M: a positive integer or a vector of d positive integers specify the maximum candidate or the given model degrees for the joint density.

• search: logical, whether to search optimal degrees between M0 and M

  or not but use M as the given model degrees for the joint density.

• mar.deg: logical, if TRUE (default), the optimal degrees are selected based on marginal data, otherwise, the optimal degrees are chosen by the method of change-point. See details.

• high.dim: logical, data are high dimensional/large sample or not if TRUE, run a slower version procedure which requires less memory

• interval: a 2 by 2 matrix, columns are the marginal supports

• B: the number of bootstrap samples and number of Monte Carlo runs for estimating p.value of the test for Hellinger correlation = 0 if test=TRUE.

• conf.level: confidence level

• integral: logical, using "integrate()" or not (Riemann sum)

• controls: Object of class mable.ctrl() specifying iteration limit and the convergence criterion eps. Default is mable.ctrl. See Details.

• progress: if TRUE a text progressbar is displayed

Returns

• eta Hellinger correlation
• CI.eta Bootstrap confidence interval for Hellinger correlation if B>0.

Details

This function calls mable.copula() for estimation of the copula density.

References

Guan, Z., Nonparametric Maximum Likelihood Estimation of Copula

See Also

mable, mable.mvar, mable.copula

Author(s)

Zhong Guan zguan@iu.edu